(c). Under a set of controlled laboratory conditions, the size of the population P of a certain bacteria culture at time t (in seconds) is given by the function P(t)= 3t² +3e' +10, t≥0.
(1) What is the size of the population after 1 minute?
(ii) Find the average rate of change of P at t = 2 and t = 6?
(iii) How fast is the size of the population changing after 1 minute?
[Verify your answer by MATHEMATICA and attach the printout of the commands and output
Answers
(i) Since P(t) gives the population of the culture after t seconds, the population after 1 second is
P(1) = 3•1² + 3e¹ + 10 = 13 + 3e ≈ 21.155
In Mathematica, it's convenient to define a function:
P[t_] := 3t^2 + 3E^t + 10
(E is case-sensitive and must be capitalized. Alternatively, you could use Exp[t]. You can also specify that the argument t must be non-negative by entering a condition via P[t_ ;/ t >= 0], but that's not necessary.)
Then just evaluate P[1], or N[P[1]] or N <at symbol> P[1] or P[1] // N to get a numerical result.
(ii) The average rate of change of P(t) over an interval [a, b} is
(P(b) - P(a))/(b - a)
Then the ARoC between t = 2 and t = 6 is
(P(6) - P(2))/(6 - 2) ≈ 321.030
In M,
(P[6] - P[2])/(6 - 2)
and you can also include N just as before.
(iii) You want the instantaneous rate of change of P when t = 60 (since 1 minute = 60 seconds). Differentiate P :
P'(t) = 6t + 3e^t
Evaluate the derivative at t = 60 :
P'(60) = 6•60 + 3e⁶⁰ = 360 + 3e⁶⁰
The approximate value is quite large, so I'll just leave its exact value.
In M, the quickest way would be P'[60], or you can differentiate and replace (via ReplaceAll or /.) t with 60 as in D[P[t], t] /. t -> 60.
Related Questions
i really dont get what math is
Answers
Answer:
the abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering ( applied mathematics ).
Step-by-step explanation:
Answer:
Math is the study of numbers, quantities, and shapes. It involves understanding and manipulating mathematical concepts and applying them to solve problems. Math is a universal language used to describe and analyze patterns and relationships in the world around us.
Step-by-step explanation:
<3
Help this is for homework and I need it right now.
Answers
Answer:
E = $9.25 * H if i havent mistaken
Find the missing side. Round to the nearest tenth.
Answers
Answer:
x = 6.89
Step-by-step explanation:
tan(19) = (x/20)
20 * tan(19) = x
x = 6.89
PLS FOR THE LOVE OF ALL THINGS HOLY HELP ME
Answers
Answer:
1. 2 2. 24 3. 8 4. 240
Step-by-step explanation:
1. 1 pen costs 2 dollars
2. 12*2=24
3. 40/5=8
4. 8*30=240
Is 48 greater that 13/25?
Answers
Answer:
yes
Step-by-step explanation:
80 is 5% of what number?
Answers
Answer:
1600
Step-by-step explanation:
1600 x 0.05 = 80
or
80 / .05 = 1600
Answer:
1600
Step-by-step explanation:
80 = 5 / 100 * x
80 * 100 = 5 * x
80 * 20 = x
x = 1600
Kendra owns a restaurant. She charges 8.20 for 2 eggs and toast. And 14.05 for 4 eggs and 3 toasts. How much does it cost for 3 eggs and 4 toast.
HELP ME PLS I BEG
Answers
Step-by-step explanation:
For 3 eggs, it would cost 24.6
For 4 toasts, it would cost 32.8
Does this help?
Please help me help help me please help me out please please help please please help me please please help
Answers
Answer:
B
Step-by-step explanation:
if q =(a,b,c,d,e) how many subsets can be obtained from the set q?
Answers
Step-by-step explanation:
n(q) = 5
Subsets = 2^n = 2^5 = 32
The value of y varies directly with x. If y=108 when x=48, what is the
value of y when x = 22?
Answers
Answer:
82 is the correct answer
2/5 is closet to 0 1/2 or 1
Answers
Answer:
2/5 is closest to 1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
2/5 = 0.4
1/2 = 0.5
Therefore closer to 1/2
Please please help please help me please please help me out
Answers
Answer:
y=1/3x+2
Step-by-step explanation:
I need help on all three problems
Answers
Solve for y.
-2+2(6y+7)=9y
y=
Answers
-2+12y+14=9y
12+12=9y
12y=9y-11
3y=-12
Y=-4
Answer:
y=-4
Step-by-step explanation:
Distribute:
−2+12+14=9
Add the Numbers:
12+12=9
Rearange the Terms:
12+12=9
Subtract 12 from both sides:
12+12−12=9−12
12=9−12
Subtract 9y from both sides:
12−9=9−12−9
3=−12
Divide both sides of the equation by the same term:
3y/3=12/3
Answer:
=−4
Find the
slope of the line
graphed below.
Answers
Answer:
2/5 sorry if im wrong:")
Step-by-step explanation:
you want to measure the volume of the vase which has an unusual shape in that it was crafted unigualyby a master bower and there is thus no mathematical formula that you can use how would you go abouy this
Answers
Simplify. Five times a number added to -2 , subtracted from triple the sum of three times the number and six.
Answers
Answer:
4x+20
Step-by-step explanation:
3(3x+6)-(5x-2)=9x+18-5x+2=4x+20
Answer:
The algebraic expression is 4x+20
what are all solutions to m•m•m=729
Answers
There's only one answer that's completely "real" ... the kind of numbers you work with every day.
That answer is:. m = 9 .
Stretch Your Thinking Joelle's cooking class is 23 times as
long as her karate class. Her cooking class starts at 4 P.M.
If her karate class is hour long, at what time does her
cooking class end? Explain.
Answers
Answer: 6 pm the next day
Step-by-step explanation:
Her karate class is 1 hour long so 1 x 23 then you add the hours starting from 5 pm.
An auditorium has 20 seats on the first row, 24 on the second row, 28 on the third row, and so on and has 30 rows of seats. How many seats are in the 30th row?
Answers
Answer:
136
Step-by-step explanation:
it adds for every time.
i need help with this question
Answers
Answer: What's the question?
Step-by-step explanation:
I need help solving this
Answers
Step-by-step explanation:
f(x) = 4x²
g(x) = x + 1
= (fog)(x)
= f( g(x) g
= 4x²
= 4(x + 1)²
Option → C
Lisa's rectangular living room is 23 feet wide. If the length is 4 feet less than twice the width, what is the area of her living room?
Answers
2w - 4
Plug in the width
2(23) - 4
Length = 42
Area: length • width
42 • 23 = 966 ft^2
possible answers: 1, 2, 3, or 4
Answers
Answer:
1
Step-by-step explanation:
BECAUSE 173.45 is a decimal and you must use a calculator to provide the answer trust me
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{173.45 = 1.7345\times10^?}[/tex]
[tex]\mathsf{1.7345\times10^? = 173.45}[/tex]
[tex]\mathsf{It\ cannot\ be: 1.7345\times10\bold{^1}\ because\ that \ gives\ you\ \boxed{\bf 17.345}}\\\large\textsf{\bf Option A isn't your answer.}[/tex]
[tex]\mathsf{173.45\neq17.345}[/tex]
[tex]\mathsf{It \could \ possibly \ be: 1.7345\times10\bold{^2}\ because\ it \ gives\ you\ \boxed{\bf 173.45}}\\\large\textsf{\bf Option B. could possibly be your answer.}[/tex]
[tex]\mathsf{173.45=173.45}[/tex]
[tex]\mathsf{It \ cannot\ be: 1.7345\times10\bold{^3}\ because\ it\ gives\ you \ \boxed{\bf 1,734.5}}\\\large\textsf{\bf Option C. isn't your answer.}[/tex]
[tex]\mathsf{173.45\neq1,734.5}[/tex]
[tex]\mathsf{It\ cannot\ be: 1.7345\times10\bold{^4}\ because\ it\ gives\ you \ \boxed{\bf 17,345}}\\\large\textsf{\bf Option D. isn't your answer}[/tex]
[tex]\mathsf{173.45\neq 17,345}[/tex]
[tex]\large\text{Based on the information we have now, we have met your answer}[/tex]
[tex]\huge\boxed{\heartsuit\ \mathsf{= 173.45 =1.7345\times10\boxed{\bf^{2}}\ \heartsuit}}[/tex]
[tex]\huge\boxed{\text{Therefore, your answer is: \boxed{\mathsf{Option\ B.\ 2}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Can someone please scallion what I have to do to get the answer? Please explain step by step to get marked!
Answers
Answer:
12,800 mL
Step-by-step explanation:
1 L = 1,000 mL
12.8 L × 1,000 mL = 12,800 mL
or
Move the decimal place 3 places to the right to get the same answer
three and fourteen thousandths written as a decimal
Answers
Answer:
0.314
Step-by-step explanation:
Answer:
3.0014
Step-by-step explanation:
How do you do and simplify 8/9 + (-5/6)
Over
1/6
These are fractions btw
Answers
Answer:
5 89/100
Step-by-step explanation:
If there is a negative sign in the denominator of any of the fractions, shift the negative sign(s) to the numerator:
-5/6=5/6
Division of fractions is equivalent to multiplication by the reciprocal of the second fraction:
5/6÷1/6=5/6×6/1
Once rearranged, multiply all of the numerators by each other. Do the same with the denominators and form a new fraction with these values:
(5 × 6) / (6 × 1) =30 / 6
The Greatest Common Factor (GCF) of 30 and 6 is 6. The result can be simplified by dividing both the numerator and denominator by 6.
30/6= (30 ÷ 6) / (6 ÷ 6) = 5
therefore..
-5/6÷1/6= 5
qns
8/9 + {(-5/6) / (1/6)} = 8/9 + 5 = 5 8/9
Combine the whole numbers and fractions together:
(0 + 5) + (8/9+0)
The whole numbers part is:
0 + 5 = 5
For the fractions part:
The Least Common Multiple (LCM) of 9 and 1 is 9. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM:
8/9+0=8/9+0 × 9=8/9+0/9
Now that the fractions have like denominators, add the numerators:
8/9+0/9=(8+0)/9=8/9
Put the whole number and fraction together:
5 +8/9=5 8/9
The result is:
8/9+5=5 8/9
$10.50 marked down 60%
Answers
Answer:
orange -> green
Step-by-step explanation:
What is the slope-intercept form of the linear equation 4x + 2y = 24?
Drag and drop the appropriate number, symbol, or variable to each box.
х
y
4
- 2
-
1
2
1
2
2
4
12
24
+
I
Answers
Answer:
The equation is y = -2x + 12.
Drag the symbol or variables y, =, -2 , x, +, 12
Step-by-step explanation:
Slope intercept form: y = mx + b.
Solve 4x + 2y = 24 for "y"
4x + 2y = 24
2y = -4x + 24
2/2y = -4/2x + 24/2
y = -2x + 12
Part A
Drag all of the steps necessary into the box to find the product of 2.3 x 0.5 using partial products.
Answers
\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]
The product of 2.3 x 0.5 using partial products is 1.15.
What is a partial products?A product obtained by multiplying a multiplicand by one digit of a multiplier having more than one digit.(So, the 2 in 23 would actually be 20.) For instance, 23 x 42 would become (20 x 40) + (20 x 2) + (3 x 40) + (3 x 2).
Given:
The given integer is
2.3 x 0.5
=23x5/100
According to given question we have
By use of partial products we get,
The partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place.
(20*00)+(20*5)+(3*00)+(3*5)
=0+100+0+15
=115
=115/100
=1.15
Therefore, the product of 2.3 x 0.5 using partial products is 1.15.
Learn more details about partial products here:
https://brainly.com/question/24716925
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