A painting sold for $264 in 1977 and was sold again in 1988 for $457. Assume that the growth in the value V of the collector's item was exponential

Answer 1

Let we start from 1977 year. So, in 1977 time t = 0.

Then we have that P₀ = P(0) = $264 and P(t) = 264e^rt;

Thenin 1988 t = 1988 - 1977 = 11 and P(11) = 264e^11r = 457; r = ln(457/264)/11 = 0.05

So, P(t) = 264e^0.05t