Question in AP CALC... rate of a rumor spreading. approx during the second week

Question

A rumor is spreading through town at a rate of t2 10t new people/day. Approximately how many people hear the rumor during the second week after it is first heard?

Answer 1

p(t)=t^2+10t

p(7)=7^2+10(7)

p(7)=49+70

p(7)=119

So in one week 119 people know.

Is the question:

How many people find out in the second week? Answer 119

How many people know by the end of the second week? Answer 119*2=238

Hope this helped. Peace

Answer 2

I'm going to assume you mean t^2 + 10t.

You're given the rate and you want the number of people.  That means integrate.  Since the second week runs from day 8 to day 14, you'll take the integral from 8 to 14 of (t^2 + 10t) dt

= (t^3)/3 + 5 t^2 from 8 to 14

= [(14^3)/3 + 5 * 14^2] - [(8^3)/3 + 5 * 8^2)]

which you can work out with a calculator, as you choose.