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Chain Rule, Log Differentiation & Rate of Change · Question 58 of 130

How fast is the population growing at t = 0?

Question 58

EasyOriginal question

A town's population $t$ years from now is modelled by $P(t) = 50{,}000\,e^{0.02t}$ .

How fast is the population growing at $t = 0$ ?

0 people per yearCorrect answerYour answer1,000 people per yearCorrect answerYour answer10,000 people per yearCorrect answerYour answer50,000 people per yearCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$P'(t) = 50{,}000 \times 0.02\,e^{0.02t} = 1000\,e^{0.02t}$ .
At $t = 0$ : $1000 \times e^{0} = 1000$ people per year.

Worth noting

50,000 is $P(0)$ , the population itself; the chain rule brings down the factor 0.02.

Concept: The rate of change of an exponential model
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsExponential and logarithmic functions

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