Question

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

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:

\(t = 0.69\)