Writing and Solving Exponential Equations: Mastery Test

The value of an autographed baseball from 2017 is $300. The value of the baseball exponentially increases by 5% each year after 2017. Write a one-variable inequality that could be used to solve for the number of years, x, it would take for the baseball to be worth at least $650. Do not use any dollar signs in the inequality. Write the inequality in standard form.

Susanna deposits $400 in a savings account with an interest rate of 3% compounded annually. What equation could Susanna use to calculate how many years it will take for the value of the account to reach $600? Fill in the values of A, b, and c to write the equation modeling this situation. C = A (b)^x

In stage 2 of a rocket's takeoff, the speed of the rocket increases at a rate of 4.3% per minute. The speed of the rocket at the beginning of stage 2 was 5,000 kilometers per hour. Its speed at the end of Stage 2 will be 25,000 kilometers per hour. If t is the time, in minutes, from the beginning of stage 2, which equation could be used to determine how long it will take for the speed of the rocket to reach 25,000 kilometers per hour, assuming it increases at the same rate for all of stage 2?

• 25,000 = 5,000(1.043)^t

• 25,000 = 5,000(1.043)^t

• 5,000 = 25,000(0.957)^t

• 5,000 = 25,000(0.043)^t

Solve the exponential equation for x. 256 = (1/4)^(3x+2)

• x = -4

• x = 4

• x = 2

• x = -2

Solve the exponential equation for x. 216 = (6^(4x+11))

• x = -3

• x = 3

• x = 2

• x = -2