let ( f(t)=5 e^{t} ).\nfor what value of ( t ) will ( f(t)=10 ) ? round to 2 decimal places.\nquestion help…

let ( f(t)=5 e^{t} ).\nfor what value of ( t ) will ( f(t)=10 ) ? round to 2 decimal places.\nquestion help: ( square ) ebook ( square ) written example

let ( f(t)=5 e^{t} ).\nfor what value of ( t ) will ( f(t)=10 ) ? round to 2 decimal places.\nquestion help: ( square ) ebook ( square ) written example

Answer

Explanation:

Step1: Set up the equation

Given ( f(t)=5e^{t}) and ( f(t) = 10), we set (5e^{t}=10).

Step2: Solve for (e^{t})

Divide both sides by 5: (e^{t}=\frac{10}{5}=2).

Step3: Take the natural logarithm

Since (y = e^{x}) and (x=\ln(y)) are inverse functions, if (e^{t}=2), then (t=\ln(2)). Using a calculator, (\ln(2)\approx0.69).

Answer:

(t = 0.69)