Question

let ( f(t)=7e^{3t}+1 ). which of the following numbers is closest to the value of ( f(5) )?

Explanation:

Step1: Substitute \(t = 5\) into the function

Substitute \(t = 5\) into \(f(t)=7e^{3t}+1\), we get \(f(5)=7e^{3\times5}+1=7e^{15}+1\).

Step2: Calculate the value of \(e^{15}\)

We know that \(e\approx2.71828\), then \(e^{15}=(e^{5})^{3}\). And \(e^{5}\approx148.413\), so \(e^{15}\approx(148.413)^{3}\approx3.269\times10^{6}\).

Step3: Calculate the value of \(7e^{15}+1\)

\(7e^{15}+1\approx7\times3.269\times 10^{6}+1 = 2.2883\times10^{7}+1\approx22883000\).

Answer:

\(22883000\)