The population of a town $t$ years from now is $P(t) = 1{,}000 + 20t + t^{2}$ . At what rate is it growing when $t = 5$ ?

30 people a yearCorrect answerYour answer31 people a yearCorrect answerYour answer45 people a yearCorrect answerYour answer1,125 people a yearCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The rate of growth is $P'(t) = 20 + 2t$ .
$P'(5) = 20 + 10 = 30$ people a year.

Worth noting

1,125 is the population at $t = 5$ , not its rate of growth.

Concept: The rate of change over time
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsRate of change of a quantity

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The population of a town ttt years from now is P(t)=1,000+20t+t2P(t) = 1{,}000 + 20t + t^{2}P(t)=1,000+20t+t2. At what rate is it growing when t=5t = 5t=5?

Explanation

The population of a town $t$ years from now is $P(t) = 1{,}000 + 20t + t^{2}$ . At what rate is it growing when $t = 5$ ?