Respuesta :
SOLUTION:
Step 1:
In this question, we are given the following:
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:
[tex]V=60(1.25)^t[/tex]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.
Step 2:
Next,
[tex]\begin{gathered} \text{Given,} \\ V=\text{ }60(1.25)^t \\ \text{Calculating the rate, } \\ we\text{ ne}ed\text{ to differentiate V with respect to t, we have that:} \\ \frac{dV}{\differentialDt t}=(1.25)^t\ln (1.25)\text{ 60} \end{gathered}[/tex]
Now, we need to evaluate:
[tex]\begin{gathered} \ln (1.25)60\text{ = 13. 38861308 }\approx\text{ 13. 3886} \\ \end{gathered}[/tex]Hence, the rate, in dollars per year since 1975, at which the price is increasing is:
[tex]\frac{dV}{\differentialDt t}=13.3886(1.25)^t[/tex]
