Edexcel IAL Mathematics P3.3.1 exponential graphs

Practise interpreting e^x graphs and exponential models, including starting values, asymptotes, limiting populations and transformed curves.

Exam points

read starting values from exponential models by substituting t=0
sketch y=e^{ax+b}+c shapes and state the horizontal asymptote
explain why a model cannot reach a target when its limiting value is too small

[Maximum number: 1]

A scientist is studying a population of fish in a lake. The number of fish, N, in the population, t years after the start of the study, is modelled by the equation

N=\frac{600 \mathrm{e}^{0.3 t}}{2+\mathrm{e}^{0.3 t}} \quad t \geqslant 0

Use the equation of the model to answer parts (a), (b), (c), (d) and (e).

Find the number of fish in the lake at the start of the study.

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P3.3.1 - function ex and its graph question 1