Question

Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s. For example, the value of a particular rocking chair is well approximated by V=50(1.65)t, where V is in dollars and t is the number of years since 1975. Find the rate, in dollars per year, at which the price is increasing.

Answer 1

we have,

we have to find the rate, in dollars per year, at which the price is increasing.

we can write,

take ln on both the side we can write,

differentiate both the side with respect to t we can write,

using chain rule we can write,

we have,

Hence,

Hence we can say that price is increasing at a rate given by,