Question

You Buy a Commemorative coin for $110. Each Year (t) the value (v) of the coin increases by 4%. Write an exponential model for this situation. Calculate the value of the coin after 3 years. When will the value of the coin will be $150?

Answer 1

Value after 3 years is `$123.74`

After 7 years and 11 months the value will be $150

Explanation:

Use the formula for exponential growth, which is the same as for compound interest:

`V = P(1 + R/100)^t`

`V = 110(1.04)^3" "larr 4%` increase per year for 3 years

`V = $123.74" "larr` the value after 3 years.

When will the value be `150?" "larr` find t

`150 = 110(1.04)^t" "larr div 110`

`150/110 = 1.04^t" "larr` log both sides

`log(15/11) = txxlog1.04`

`log(15/11) div log 1.04 = t" "larr` use a calculator

`7.9079 = t ~~7 10.9/12`

After 7 years and 11 months the value will be $150