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)