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

		-0.308
		1.7
		0.308
		0.5

Question 2

Solve for x. 3^x = 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) = 5^x-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=b^x is equivalent to the logarithmic equation x=log_by

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.

4^2x-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 e^kt

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) = 0.5^x 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.