exponential decay time

Practise exponential decay time with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

A sensor model gives $M(t)=360e^{-\frac{1}{3}t}$ for $t\geq0$. Find the exact time when $M(t)=\frac{360}{e^{2}}$.

Worked explanation

• Divide by the initial amount

  $e^{-\frac{1}{3}t}=e^{-2}$.

• Take natural logarithms

  $-\frac{1}{3}t=-2$.

• Solve and check

  The time is 6 hours; substituting it into the model gives the required value.

$t=6$ hours.

Original VectorPaths practice; not an official VCAA question or marking rubric.