Grantham University Algebra: Continuously Compounded Interest Homework

Question 1

Evaluate the function at the indicated value of x. Round your result to three decimal places.

Function: f(x) =

0

.5

^x Value: x =

1.

7

–

0.

3

08

1.7

0.308

0.5

Question 2

Solve for x. 3x = 81

7

3

4

-3

Question 3

Logarithms are the inverse of exponentials.

True

False

Question 4

The Logarithm Quotient Rule states:

logb(x / y) = logb(x) + logb(y)

logb(x / y) = logb(x) – logb(y)

logb(x y) = y ∙ logb(x)

logb(c) = 1 / logc(b)

Question 5

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. Assume all variables are positive.

log3 9x

log3 9 * log3 x

log3 9 + log3 x

log3 9 – log3

none of these

Question 6

Select the graph of the function. Indicate which graph is correct: 1st, 2nd, 3rd, or 4th f(x) = 5x-1

Question 7

Evaluate the function at the indicated value of x. Round your result to three decimal places. Show your work

Value: x=2

Question 8

The exponential equation y=bx is equivalent to the logarithmic equation x=logby

True

False

Question 9

Use the One-to-One property to solve the equation for x.

e(3x+5) = e6

x = -1/3

x2 = 6

x = 1/3

x = 3

Question

10

Write the logarithmic equation in exponential form.

log8 64 = 2

82 = 16

82 = 8882 = 64

864 = 2

Question 11

Write the exponential equation in logarithmic form.

43 = 64

log64

=

log4 64 = 3log4 64 = -3

log4 3 = 64

4	3

Question

12

The given x-value is a solution (or an approximate solution) of the equation.

42x-7 = 16

x = 5

True False

Question 13

Find the magnitude R of each earthquake of intensity I (let I0=1). (Hint: R=log (I/I0)

I = 19000

3.28

5.28

4.28

2.38

Question 14 – show you work

pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the hydrogen ion concentration. The equation is: pH = – log [H+] If an acid has an H+ concentration of 10-4, what’s the pH?

Question 15 – show your work

A general formula for exponential Growth can be given by: A = P ekt In your textbook, or using another reliable source, research what values, P, A, k and t represent and write your answer. (Hint: What do each of the variables stand for?)

Question 16 – show your work

Continuously compounded interest means your principal is earning interest and you keep earning interest on the interest earned. Research the formula for Continuously Compounded Interest and write it below.

Question 17

$2500 is invested in an account at interest rate r, compounded continuously. Find the time required for the amount to double. (Approximate the result to two decimal places.)

r = 0.0570

13.16 years

10.16 years

11.16 years

12.16 years

Question 18 – show your work

Write Eulers Number (e) to three decimal places.

Question 19 – show your work

Exponential functions often involve the rate of increase or decrease of something such as a population, for example. If there is a population increase, it is a _______ function and when there is a decrease, it is a ________ function.

Question 20

Solve for x: log(3x−2)−log(2)=log(x+4)

10

04

12

Question 21

Evaluate the function at the indicated value of x. Round your result to three decimal places.

Function: f(x) = 0.5x Value: x = 1.7

-0.308

1.70.308

0.5

Question 22

Select the graph of the function. Indicate which of the graphs below is the correct one: 1st, 2nd, 3rd, or 4th.

Question 23

$5000 is put into an account that pays 4% interest compounded continuously. How much will be in the account after 3 years? Round the answer to the nearest whole number.

5637

5637.5

5638

5638.5

Question 24 – show your work

Given the equation: y = 50(2.5)x, what is the value of y (to the nearest tenth) when x = 3? Next, tell us if the equation represents growth or decay. Question 1
Evaluate the function at the indicated value of x. Round your result to three decimal places.
Function: f(x) = 0.5^x Value: x = 1.7
-0.308
1.7
0.308
0.5
Question 2
Solve for x. 3x = 81
7
3
4
-3
Question 3
Logarithms are the inverse of exponentials.
True
False
Question 4
The Logarithm Quotient Rule states:
logb(x / y) = logb(x) + logb(y)
logb(x / y) = logb(x) – logb(y)
logb(x y) = y ∙ logb(x)
logb(c) = 1 / logc(b)
Question 5
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of
logarithms. Assume all variables are positive.
log3 9x
log3 9 * log3 x
log3 9 + log3 x
log3 9 – log3
none of these
Question 6
Select the graph of the function. Indicate which graph is correct: 1st, 2nd, 3rd, or 4th
f(x) = 5x-1
Question 7
Evaluate the function at the indicated value of x. Round your result to three decimal places. Show your work
Value: x=2
Question 8
The exponential equation y=bx is equivalent to the logarithmic equation x=logby
True
False
Question 9
Use the One-to-One property to solve the equation for x.
e(3x+5) = e6
x = -1/3
x2 = 6
x = 1/3
x=3
Question 10
Write the logarithmic equation in exponential form.
log8 64 = 2
82 = 16
82 = 88
82 = 64
864 = 2
Question 11
Write the exponential equation in logarithmic form.
43 = 64
log64

4

= 3
log4 64 = 3
log4 64 = -3
log4 3 = 64
Question 12
The given x-value is a solution (or an approximate solution) of the
equation.
42x-7 = 16
x=5
True
False
Question 13
Find the magnitude R of each earthquake of intensity I (let I0=1). (Hint:
R=log (I/I0)
I = 19000
3.28
5.28
4.28
2.38
Question 14 – show you work
pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the
hydrogen ion concentration. The equation is:
pH = – log [H+]
If an acid has an H+ concentration of 10-4, what’s the pH?
Question 15 – show your work
A general formula for exponential Growth can be given by:
A = P ekt
In your textbook, or using another reliable source, research what values, P, A, k and t represent and write
your answer. (Hint: What do each of the variables stand for?)
Question 16 – show your work
Continuously compounded interest means your principal is earning interest and you keep earning interest on
the interest earned. Research the formula for Continuously Compounded Interest and write it below.
Question 17
$2500 is invested in an account at interest rate r, compounded
continuously. Find the time required for the amount to
double. (Approximate the result to two decimal places.)
r = 0.0570
13.16 years
10.16 years
11.16 years
12.16 years
Question 18 – show your work
Write Eulers Number (e) to three decimal places.
Question 19 – show your work
Exponential functions often involve the rate of increase or decrease of something such as a population, for
example. If there is a population increase, it is a _______ function and when there is a decrease, it is a ________
function.
Question 20
Solve for x: log(3x−2)−log(2)=log(x+4)
10
0
4
12
Question 21
Evaluate the function at the indicated value of x. Round your result to three decimal places.
Function: f(x) = 0.5x Value: x = 1.7
-0.308
1.7
0.308
0.5
Question 22
Select the graph of the function. Indicate which of the graphs below is the correct one: 1st, 2nd, 3rd, or 4th.
Question 23
$5000 is put into an account that pays 4% interest compounded continuously. How much will be in the
account after 3 years? Round the answer to the nearest whole number.
5637
5637.5
5638
5638.5
Question 24 – show your work
Given the equation: y = 50(2.5)x, what is the value of y (to the nearest tenth) when x = 3? Next, tell us if the
equation represents growth or decay.