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.

Question

Nora Shelton

Mathematics

3 March, 16:42

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.

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Answers (1)

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Elaina Buchanan · Answer 1

General exponential equation

y = A (1+r) ^x

where

A = initial value

r = rate increase (+) or decrease (-)

x = time period of the change

y = projected value

y = 300 (1.05) ^x

in this problem, x = years after 2017

we want to find an x that makes the value more than or equal to 650

650 < = 300 (1.05) ^x