Question 1

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

Function: f(x) = 0.5^xValue: 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:

log_b(x / y) = log_b(x) + log_b(y)

log_b(x / y) = log_b(x) - log_b(y)

log_b(x^y) = y log_b(x)

log_b(c) = 1 / log_c(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.

log₃9x

log₃9 x log₃x

log₃9 + log₃x

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.

f(x)=500e(.05)^xValue: x=2

Question 8

The exponential equationy=b^xis equivalent to the logarithmic equationx=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.

log₈64 = 2

8²= 16

8²= 88

8²= 64

8⁶⁴= 2

Question 11

Write the exponential equation in logarithmic form.

4³= 64

log₆₄4 = 3

log₄64 = 3

log₄64 = -3

log₄3 = 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

pHis a measure of the hydrogen ion concentration of a solution. It isdefined as the negative logarithm of the hydrogen ion concentration.The equation is:

pH = - log [H⁺]

If an acid has anH⁺concentration of 10^-4, what'sthe pH?

Question 15

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 answer. (Hint: What do each of the variables stand for?)

Question 16

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

Write Eulers Number (e) to three decimal places.

Question 19

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.