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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.

Sagot :

Answer: [tex]30e^{0.00813x}[/tex]

Step-by-step explanation:

Given

Median age in 1980 is [tex]30[/tex]

It is [tex]35.3[/tex] in year 2000

Suppose the median age follows the function [tex]ae^{bx}[/tex]. Consider 1980 as starting year. Write the equation for year 1980

[tex]\Rightarrow 30=ae^{b(0)}\\\Rightarrow 30=a[/tex]

For year 2000

[tex]\Rightarrow 35.3=30e^{20b}\\\\\Rightarrow \dfrac{30e^{20b}}{30}=\dfrac{35.3}{30}\\\\\Rightarrow e^{20b}=1.17666\\\\\Rightarrow b=0.00813[/tex]

After t years of 1980

[tex]\Rightarrow 30e^{0.00813x}[/tex]

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