Question

4. Gina bought a computer for $1,500. Its value is depreciating at an annual rate of 15%

per year. Fill in the blank to complete the sentence.
To the nearest tenth of a year, it will take
lose half of its value.
years for Gina's computer to loose half its value?

Answer 1

To find the number of years it will take for Gina's computer to lose half of its value, we can use the half-life formula for exponential decay:

t = (ln 2) / r

where t is the half-life, r is the annual rate of depreciation (expressed as a decimal), and ln 2 is the natural logarithm of 2, which is approximately 0.693.

Substituting the given values, we get:

t = (ln 2) / 0.15 ≈ 4.6 years

Therefore, to the nearest tenth of a year, it will take 4.6 years for Gina's computer to lose half its value.