# The projected year-end assets in the Social Security trust funds, in trillions of dollars, where...

## Question:

The projected year-end assets in the Social Security trust funds, in trillions of dollars, where {eq}t{/eq} represents the number of years since 2000, can be approximated by {eq}A(t) = 0.0000329t^3 - 0.00450t^2 + 0.0613t + 2.34{/eq},

where {eq}0 \leq t \leq 50{/eq}.

a. Where is {eq}A(t){/eq} increasing?

b. Where is {eq}A(t){/eq} decreasing?

## Rate of Change:

To solve this question, we need to understand that a function will increase in value when the changes in its value are positive and will be decreasing in value when the changes in its value are negative. The rate of change of a function is given by its derivative. So, we need to analyze its derivative.

a)

The function will be increasing when its first derivative is positive.

{eq}\displaystyle A'(t)=\frac{\mathrm{d} }{\mathrm{d} t} \left...

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