A shop's total sales $t$ months after opening are $S(t) = 200t + 5t^{2}$ units. At what rate are sales growing at $t = 4$ ?

210 units a monthCorrect answerYour answer220 units a monthCorrect answerYour answer240 units a monthCorrect answerYour answer880 units a monthCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The rate is $S'(t) = 200 + 10t$ .
At $t = 4$ : $200 + 40 = 240$ units a month.

Worth noting

880 is $S(4)$ , the total sold, not the rate.

Concept: The rate of change over time
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsRate of change of a quantity

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A shop's total sales ttt months after opening are S(t)=200t+5t2S(t) = 200t + 5t^{2}S(t)=200t+5t2 units. At what rate are sales growing at t=4t = 4t=4?

Explanation

A shop's total sales $t$ months after opening are $S(t) = 200t + 5t^{2}$ units. At what rate are sales growing at $t = 4$ ?