## Related questions with answers

The aged dependency ratio is defined as the number of individuals age $65$ or older per $100$ individuals ages $20-64$. The aging of the baby boomer generation along with medical advancements and lifestyle changes for all individuals have caused this ratio to rise, shaping society's plans for the needs of a greater number of older individuals. By using Social Security Administration data for selected years from $1990$ and projected to $2045$, the aged dependency ratio can be modeled by the function

$A(t)=-0.000497 t^3+0.0449 t^2-0.669 t+22.3$

where $t$ is the number of years past $1990$.

(a) Find the critical points for this model, and classify them as relative maxima or relative minima.

(b) Interpret the points found in part (a)

Solution

Verified(a). To find the critical points, we need to find the derivative of the given function and equate it to zero.

$\begin{aligned} A(t)&=-0.000497t^3+0.0449t^2-0.669t+22.3\\ A'(t)&=\frac{d(-0.000497t^3+0.0449t^2-0.669t+22.3)}{dt}\\ &=-\frac{1491t^2}{1000000}+\frac{449t}{5000}-\frac{669}{1000}\\ &=-\frac{1491t^2-89800t+669000}{1000000} \end{aligned}$

## Create an account to view solutions

## Create an account to view solutions

## More related questions

1/4

1/7