Determine an exponential model from data

Practise determine an exponential model from data with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

A culture is modelled by $N(t)=Ae^{kt}$, where t is in hours. Initially $N(0)=80$ and $N(3)=160$. (a) Find A and k exactly. [2 marks] (b) Find the time when $N(t)=640$. [2 marks]

Worked explanation

• Part (a)

  At $t=0$, $A=80$. Then $80e^{3k}=160$ implies $3k=\ln2$.

• Part (b)

  $e^{kt}=8$ gives $t=\ln8/(\ln2/3)=9$.

(a) $A=80$, $k=\ln2/3$.; (b) $9$ hours.

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