Question

Frankie made a poor investment in a particular baseball card collection. The value of the collection has decreased by 2.9% since he purchased it. If this trend continues, approximately how long will it be before the collection is worth half of its original value? Round your answer to the nearest whole year.

years

Answer 1

Explanation:

If the value of the collection has decreased by 2.9% since Frankie purchased it, this means that the current value is 97.1% of the original value (100% - 2.9% = 97.1%). Let's use "x" to represent the number of years it will take for the collection to be worth half of its original value.

We can use the following equation to solve for x:

(0.971)^x = 0.5

Taking the logarithm of both sides, we get:

x*log(0.971) = log(0.5)

Solving for x, we get:

x = log(0.5) / log(0.971)

x ≈ 23.7

Therefore, it will take approximately 24 years for the collection to be worth half of its original value. Rounded to the nearest whole year, the answer is 24.