Question

he 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.

Answer 1

If the ball increases by 5% each year, then it's value over t years would be:
fv=300*(1+.05)^t, where fv is future value. So:
300*(1.05)^t=650
1.05^t=2.166667
t=15.85 years
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Answer 2

`300(1.05)^x\geq 650`

Explanation:

Since, the initial value of the basketball = $ 300

Annual rate of interest = 5 %

Let the basket ball after x years is worth at least $ 650,

⇒ The cost of basketball after x years ≥ 650

`\implies 300(1+(5)/(100))^x\geq 650`

`\implies 300(1+0.05)^x\geq 650`

`\implies 300(1.05)^x \geq 650`

Which is the required inequity.