# 26. The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be...

## Question:

26. The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be growing at the rate of

R(t) = 0.063t -0.48t + 3.87 {eq}(0\leq t \leq 15) {/eq}

million people/decade, where t is measured in decades, with t = 0 corresponding to 1900, t How many times faster will the average rate of growth of U.S. citizens aged 65 yr and older between 2000 and 2050 be than that between 1940 and 1990. (Round your answer to two decimal places.)

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27. The manager of TeleStar Cable Service estimates that the total number of subscribers to the service in a certain city t years from now will be

{eq}N(t) = \frac{40,000}{\sqrt{1 + 0.2t}} + 60,000. {/eq}

Find the average number of cable television subscribers over the next 6 years if this prediction holds true. (Round your answer to the nearest integer.)

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## Average Rate of Change:

This problem involves finding the average rate of change of the given functions. The average rate of change is defined by the formula -

{eq}\displaystyle <f> = \frac{ \Delta N}{\Delta T} {/eq}

But since the function is given as a function of time, thus to find the change in net sum, we have to integrate the equation. Thus, we have -

{eq}\displaystyle <f> = \frac{ \int f(t) dt}{\int dt} {/eq}

## Answer and Explanation:

(1) The number of US citizens aged 65 years and older from 1990 through 2050 is estimated to be growing at a rate of -

{eq}\displaystyle R(t) =...

See full answer below.

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