The exponential function given by $H(t)=80,030.87(1.0486)^{t}$, where $t$ is the number of years after 2003 , 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 2008 and in 2030. The centenarian population in 2008 is approximately 101463. (Round to the nearest whole number.) The centenarian population in 2030 is approximately (Round to the nearest whole number.)
Solution
Step 1 ：The exponential function given by \(H(t)=80,030.87(1.0486)^{t}\), where \(t\) is the number of years after 2003, can be used to project the number of centenarians in a certain country. We are asked to use this function to project the centenarian population in this country in 2008 and in 2030.
Step 2 ：To find the population in 2008, we need to substitute \(t=2008-2003=5\) into the function. Similarly, to find the population in 2030, we need to substitute \(t=2030-2003=27\) into the function.
Step 3 ：After substituting these values into the function, we will round the results to the nearest whole number to get the final answer.
Step 4 ：The centenarian population in 2008 is approximately \(\boxed{101463}\).
Step 5 ：The centenarian population in 2030 is approximately \(\boxed{288220}\).
