Question

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.

Answer 1

For this case we have a function of the form:

$y = A * (b) ^ x$

Where,

A: initial value of an autographed baseball

b: growth rate

x: number of years

Substituting values we have:

$y = 300 * (1.05) ^ x$

For the moment when the value is at least 650 $ we have the following inequality:

$300 * (1.05) ^ x \geq 650$

Answer:

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 is:

$300 * (1.05) ^ x \geq 650$

Answer 2

For this case we have a function of the form:

$y = A * (b) ^ x$

Where,

A: initial value of an autographed baseball

b: growth rate

x: number of years

Substituting values we have:

$y = 300 * (1.05) ^ x$

For the moment when the value is at least 650 $ we have the following inequality:

$300 * (1.05) ^ x \geq 650$

Answer:

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 is:

$300 * (1.05) ^ x \geq 650$