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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=150(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.

Verified Answer :

Answer:

The price is increasing by 65% per year.

Step-by-step explanation:

Since, the exponential growth function,

\(f(x) = a(1+r)^x\)

Where,

a = initial value,

r = rate of increasing per period,

x = number of periods,

Here, the given function,

\(V=150(1.65)^t\)

\(\implies V=150(1+0.65)^t\)

Where,

t = number of years,

By comparing,

r = 0.65,

i.e. the rate of increasing per year = 0.65 = 65%

Comparing to a standard exponential function, it is found that the price is increasing at a rate of 65% per year.

An increasing exponential function is modeled as follows:

\(V(t) = V(0)(1 + r)^t\)

In which:

  • V(0) is the initial value.
  • r is the increase rate, as a decimal.

In this problem, the equation is:

\(V(t) = 150(1.65)^t\)

Comparing to the standard equation, we have that:

\(1 + r = 1.65\)

\(r = 0.65\)

Thus:

The price is increasing at a rate of 65% per year.

A similar problem is given at https://brainly.com/question/24282972

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