Question

In 1980, the median age of the U.S. population was 30.0; in 2000, the median age was 35.3. Consider 1980 as the starting point (time zero) for this problem. Create an explicit exponential formula for the median age of the U.S. population t years after 1980, assuming the median age has exponential growth.

Answer 1

Answer:
`30e^(0.00813x)`

Explanation:

Given

Median age in 1980 is
`30`

It is
`35.3` in year 2000

Suppose the median age follows the function
`ae^(bx)`. Consider 1980 as starting year. Write the equation for year 1980

`\Rightarrow 30=ae^(b(0))\\\Rightarrow 30=a`

For year 2000

`\Rightarrow 35.3=30e^(20b)\\\\\Rightarrow (30e^(20b))/(30)=(35.3)/(30)\\\\\Rightarrow e^(20b)=1.17666\\\\\Rightarrow b=0.00813`

After t years of 1980

`\Rightarrow 30e^(0.00813x)`