Answer:
101.76
Step-by-step explanation:
Suppose that $10,083 is invested at an interest rate of 6.8% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answer:
a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]
b)
The balance after 1 year is of $10,768.644
The balance after 2 years is of $11,500.91
The balance after 5 years is of $14,010.25.
The balance after 10 years is of $19,467.15
c)
The doubling time is of 10.54 years.
Step-by-step explanation:
Continuously compounded interest:
The amount of money earning after t years, with interest compounded continuously, is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.
a) Find the exponential function that describes the amount in the account after time t, in years.
Suppose that $10,083 is invested at an interest rate of 6.8% per year
This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 10083(1+0.068)^t[/tex]
[tex]A(t) = 10083(1.068)^t[/tex]
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
After 1 year:
[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]
The balance after 1 year is of $10,768.644
After 2 years:
[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]
The balance after 2 years is of $11,500.91.
After 5 years:
[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]
The balance after 5 years is of $14,010.25.
After 10 years:
[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]
The balance after 10 years is of $19,467.15.
c) What is the doubling time?
This is t for which [tex]A(t) = 2A(0)[/tex]. So
[tex]A(t) = A(0)(1.068)^t[/tex]
[tex](1.068)^t = 2[/tex]
[tex]\log{(1.068)^t} = \log{2}[/tex]
[tex]t\log{1.068} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]
[tex]t = 10.54[/tex]
The doubling time is of 10.54 years.
Mr. & Mrs. Dargen spent $46.25 on a meal, about how much should they
leave for a 18% tip?
Answer:
$8.32
Step-by-step explanation:
I found one percent of 46.25 ( which was 0.4625) by dividing it by 100 then i multiplied that number by 18 in order to get how much the 18% tip would be. From that I got 8.325 but since this is in a currency the answer would be 8.32
thats just how I do it there's other ways
There are two cylinders.
The first has a radius of 7 and height of 5.
The second has a radius of 6 and height of 7.
Which cylinder has the larger surface area?
A-The first cylinder
B-The second cylinder
Answer:
b
Step-by-step explanation:
13 points Please help 8th grade math
Answer:
4.2
Step-by-step explanation:
Answer:
Volume of the sphere is 2065.24
I have no idea how to calculate the slope of that.
Step-by-step explanation:
3·π·7.93≈2065.23693
= REAL NUMBERS Evaluating a quadratic expression: Integers Evaluate the expression when n=4. n2-5n+6
Answer:
-2
Step-by-step explanation:
I got it wrong and it told me negative 2 was the correct answer lol
Find the measure of 26.
4 6 = [?]
249
46
Answer:
Solution given:
<6+24=180[co- interior angle]
<6=180-24=156°
<6=156°
HELP! WILL GIVE BRANLIEST!
Answer:
Z = 80 degrees and X = 8 degrees
Step-by-step explanation:
The reason Z = 80 degrees is because a flat line always has a measure of 180 degrees.
I forget the term, but we know that 6x + 52 is equal to 100 due to some angle theorem. (Once again, I do not remember the term.)
We then subtract 52 from 100 to get the equation 6x = 48. Divide them both by 6 and you get X = 8!
Hope this helped!
a continuous function is differentiable.true or false?
Answer:
false
Step-by-step explanation:
its equal every time because its countinuous
12 cm
16 cm
find the lateral area surface area is each regular pyramid round to the nearest 10th if necessary
Single term algebraic expression is called?
Monomial
Binomial
Trinomial
None of these
also I am groot friend me
[tex]single \: term \: expression \: is \: called[/tex]
[tex]monomial[/tex]
The weight of an object on the moon, m, is about of the object's weight on Earth, e
Which equation represents the approximate weight of an object on the moon in terms
of the object's weight on Earth?
A m =
Bm
8
Gm6e
Dm66
Students crew anywhere on this side
Answer:
wdDW
Step-by-step explanation:
WDDwdWD
Help me please this is due tonight!
Here is a photo of the problem. I’m a little blank on my math tonight, any help is appreciated!
9514 1404 393
Answer:
A
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
__
Using these rules, along with the distributive property, we can simplify the given expression.
[tex]\displaystyle 9a^3b^6(3a^3b^2+7a^2b^2)-(5a^4b^4)^2\\\\=\displaystyle 9a^3b^6(3a^3b^2+7a^2b^2)-(5^2a^{4\cdot2}b^{4\cdot2})\\\\=(9)(3)a^{3+3}b^{6+2}+(9)(7)a^{3+2}b^{6+2}-25a^8b^8=27a^6b^8+63a^5b^8-25a^8b^8\\\\=\boxed{-25a^8b^8+27a^6b^8+63a^5b^8}\qquad\text{matches A}[/tex]
21 and 22 are complementary angles. The measure of Z1 is 60°. The
measure of 22 is 5(x - 1)º. Find the value of x.
Answer:
The value of x is 7
Step-by-step explanation:
Complementary angles have a sum of 90°, therefore the equation to solve for x is:
∠1+∠2=90°
60°+5(x-1)°=90°
5(x-1)=30°
x-1=6
x=7
So the value of x is 7
How many different 5-letter words can be made
a. if the first letter must be A or Y and no letter may be repeated?
b. if repeats are allowed (but the first letter is A or Y)?
c. How many of the 5-letter words (starting with A or Y) with no repeats end
in H?
Fort his problem what is the correct answer?
Answer:
its b have a nice day
Step-by-step explanation:
Answer:
I think its D.
Step-by-step explanation:
100 points What is the equation of the line that goes through (1,-1) and is parallel to y =
3x-3?
A. y+ 1 = 3(x - 1)
B. y+1=-}(-1)
C. y = 3x + 1
OD. y+1-}(x-1)
the product of 23
and 20
HELPPPP. QUICKK. PLEASEE AND TY :))
Answer: D
Step-by-step explanation:
D
  help needed pls
Marie bicycled 15 miles at 5 miles per
hour. How long did Marie bicycle?
Answer:
3 hours
Step-by-step explanation:
15÷5=3 so that's ot
Which statement is true about the relationship between the height of the plant and the number of days? This relationship is a function because the plant can only be one height at a time. This relationship is not a function because the plant can only be one height at a time. This relationship is a function because the plant can be more than one height at a time. This relationship is not a function because the plant can be more than one height at a time.
Answer:
This relationship is a function because the plant can only be one height at a time.
Step-by-step explanation:
Functions occur when the recorded x-value is varied each time. Since the height of the plant (the x-value) varies each day, it is a function.
The table shows how much Li earns for moving different numbers of lawns. Write an algebraic expression that describes the total earnings for n lawns.
Answer:
15n
Step-by-step explanation:
Given
The above table
Required
The formula of the table
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{n_2 - n_1}[/tex]
Where:
n = Number of Lawns
y = Earnings
[tex](n_1,y_1) = (2,30)[/tex]
[tex](n_2,y_2) = (5,75)[/tex]
So, we have:
[tex]m = \frac{75 - 30}{5 - 2}[/tex]
[tex]m = \frac{45}{3}[/tex]
[tex]m = 15[/tex]
The equation is then calculated as:
[tex]y = m(n- n_1) + y_1[/tex]
This gives:
[tex]y = 15(n- 2) + 30[/tex]
[tex]y = 15n- 30 + 30[/tex]
[tex]y = 15n[/tex]
Hence:
B is correct
PLS HELP I WILL MARK BRAINLIEST
Four more than 5 times the number x is less than 50. Write an inequality for this statement.
Answer:
5x<50
Step-by-step explanation:
Answer:
Step-by-step explanation:
5n < 50 <--- subtracts 4 from both sides
n < 10 <--- divides both sides by 5
Check: testing n=0, we have 4 + 5(0) = 4 + 0 = 4 < 54, so yes it works
testing n=10, 4 + 5(10) = 4 + 50 = 54.
testing n=11, 4 + 5(11) = 4 + 55 = 59 <--- fails as expected.
X < 10, proven, verified, correct
PLEASE HELP ASAP!
Classify the polynomial, 8m^3–10m^2– 7, by degree and number of terms.
Answer:
Step-by-step explanation:
The answer is m • (2m - 3) • (4m + 1)
How -15 + 8 gives me 7 ????????
Answer:
It gives you -7
Step-by-step explanation:
Think of the problem as 8 - 15, because 8 is a smaller number and 15 is bigger, you'll get a negative number.
The next step is use the rule**a-b = -(b-a)**which is - (15 - 8)
Then when you simplify it, it will be - (15 - 8)= - 7**(which is the answer)
Hope this helps:)
What is the solution to
−12x≤−72
How is x = 5 mathematically different from x > 5?
Answer:
in x>5 x is larger than 5
Step-by-step explanation:
x=5 means x is equal to 5
x>5 means x is greater than 5
Answer:
X=5 means that the unknown variable in the equation is equal to the number 5, while x > 5 means that the unknown variable is larger then the number 5.
Step-by-step explanation:
Find (-5)(-2)(5)( - 1)(-4)
Tucker purchased $4,600 in new equipment for a catering business. He estimates that the value of the equipment is reduced by approximately 40% every two years. Tucker states that the function V(t)=4,600(0.4)2t could be used to represent the value of the equipment, V, in dollars, t, years after the purchase of the new equipment. Explain whether the function Tucker stated is correct, and, if not, determine the correct function that could be used to find the value of the equipment purchased.
Simplify the expression -3 devided by -2/5. A. -7 1/2 B. -1 1/5 C. 1 1/5 D. 7 1/2
Answer:
D. 7 1/2
Step-by-step explanation:
-3 divided by -2/5
-(-3(-5/2)
-(-3 x 5/2)
-15/2
7 1/2
Hope it helps
