Question

A rare stamp in Lings collection is now worth $280. it's value has been increasing by 8% each year. the value of the stamp to continue increasing at this rate, so the function V(t) =280(1.08)^t estimates the value of GLing expects after t years.Ling graphed the function to find the number of years, to the nearest whole number, that he must wait before the stamp is worth approximately double it's current value.How many years will it take for the stamp to double in value?

Answer 1

9 years

1) Gathering the data

now worth $280

increasing by 8% each year.

V(t) =280(1.08)^t

2) Since we want to know how long it'll take for that stamp to double its value then we can write:

`\begin{gathered} 280*2=560 \\ 560=280(1.08)^t \\ (560)/(280)=(280(1.08)^t)/(280) \\ 2=(1.08)^t \\ \log _(1.08)(1.08)^t=\log _(1.08)2 \\ t\log _(1.08)(1.08)^{}=\log _(1.08)2 \\ t=\log _(1.08)2 \\ t\approx9.00 \end{gathered}`

Notice that we had to apply the logarithms on both sides and we chose an appropriate base so that we can get rid of that 1.08 on the left side.

3) So, in approximately 9 years that stamp will have its current value doubled.