Question

11. The exponential function given by ​H(t)=80,030.83​(1.0481​)t​, where t is the number of years after 2010​, can be used to project the number of centenarians in a certain country. Use this function to project the centenarian population in this country in 2013 and in 2038.

Answer 1

A function assigns the value of each element of one set to the other specific element of another set. The number of centenarians in the country in 2013 is 9.4175×10⁴⁵.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The exponential function that can be used to project the number of centenarians in a certain country is $H(t) = 80,030.83(1.0481)^t$.

Now, the number of centenarians in the country in 2013 is,

$H(t) = 80,030.83(1.0481)^t\\\\H(2013) = 80,030.83(1.0481)^{2013}\\\\H(2013) = 9.4175 \times 10^{45}$

Also, the number of centenarians in the country in 2038 is,

$H(t) = 80,030.83(1.0481)^t\\\\H(2038) = 80,030.83(1.0481)^{2038}\\\\H(2038) = 3.048 \times 10^{46}$

Hence, the number of centenarians in the country in 2013 is 9.4175×10⁴⁵.

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