Unit Four

Exponent Rules

100

Name one equation that is equivalent to x^-4/3 for all when x is not equal to 0?

1/cube root of x^4

200

If x>0, then the expression ((x³)^-2)⁵ is equivalent to-

1/x³⁰

300

If x>0 and x^-1/4 state an equation that is equivalent.

1/root to the fourth of x

400

If x>0, then the expression ((x^-4)^-1)⁶ is equivalent to-

x²⁴

500

Which of the following is the solution to the equation shown below in terms of the unknown constant k? (14)2x-3k=164x+k

What is x=k/10?

Exponential Graphs

100

 What is the inverse of y=log8x?

8^x

200

What is the domain of y=logx in interval notation?

[0,∞)

300

Given the graph of the exponential function y=a(b)^x shown below, which of the following statements must be true? Refer to graph 2.

a<10 b<1

400

Given that graph of y=a(b)^x shown, which of the following must be true? Refer to Graph 1.

A is greater than 5 and B is greater than 1

500

Given that the graph of y=a(b)^x is shown, which of the following must be true? Refer to graph 3.

a<0 and 0<b<1

Logarithms

100

Which of the following is the value of log_b(1/b³) for any base b>0?

-3

200

For which value of x is the expression log₇(2x-3) undefined?

1

300

If the equation 3(5)^2x = k is solved for x in terms of k, the result is-

x=1/2log₅ (k/3)

400

Which of the following is the solution to the equation 8^x-2a=(12)^5a in terms of the unknown constant a?

x=1/3a

500

If a(b)^x-c = d then x = ?

log_b(d/a)+c

Percent Change/Cooling

100

If a population is increasing at a constant rate of 2.4% per year, by what percent will it increase in 10 years?

26.8%

200

If a car’s value is decreasing at a constant rate of 4% per year, by which percent will it decrease in 8 years?

27.9%

300

If Miya places $650 in a savings account that earns a nominal 2.5% yearly interest compounded monthly, then which of the following is closest to the worth of this account after 4 years?

$718.29

400

What percent below is closest to the annual percent increase that will allow a town’s population of 25,000 to increase to 34,000 over an 8-year period?

3.9%

500

The population of fish in a local bay is modeled by the equation 

P(t) =2,500(1.025 )^t , where t represents the number of years since 2,500 fish were first measured. Based on this equation, which of the following represents the percent the population will grow in a decade?

28%

Exponents

100

Which of the following is equivalent to a^2/3 for all values of a?

cube root of a²

200

If g(x)=4(3)^x then g(-2)=?

4/9

300

Given the graph of the exponential function y=a (b)^x shown below, which of the following statements must be true?

A is less than 5 and B is less than one

400

If f(x)=20(2)^x then f(-3)=?

5/2

500

In the exponential function h (t)= a (b)^t it is known that h (4)=6 and h (8)=0.5. Which of the following is closest to the value of b?

0.54