Question

Five years ago, you purchased a baseball card for $5.97. Unforunately, the value of the card has been declining at a rate of 2% each year. How many years will it take for the card to be worth half as much as it was five years ago?

Answer 1

Answer: 35 years

Explanation:

V= value

The half value can be determined by multiplying 5.97 * (1-0.02)ⁿ

n stands for the amount of years.

(1-0.02) is the formula for finding the 2% rate

now, we want to find half the value by multiplying by 1/2 or .5

0.5*597=597* (1-0.02)ⁿ

now, to solve for n

0.5=(1-0.02)ⁿ

take the natural logarithm of both sides

In(0.5)=((1-0.02)ⁿ)

use the properties of logarithm to bring the exponents down

In(0.5) = n*In(0.98)

Divide both sides by In(0.98)

n ≈ 34.62