I need help w/: Pop. increases at rate of r(t)= (3.62)(1+0.8t^2) people per year

[KFS]

Hello. This is the problem: The population of Booneville increases at a rate of r(t)= (3.62)(1+0.8t^2) people per year, where t is the time in years from 1970. The population in 1976 was 726. What was is it in 1984?
I' ve been trying integrating and then evaluating the integral at t=8 (8 years, 1984-1976=8). The answer must be approx. 3195. I want to learn this because I saw the next problems in my textbook are similar to this one. It might be silly, but any help is welcome.
Thank you.

 

[Dr.Peterson]

Hello. This is the problem: The population of Booneville increases at a rate of r(t)= (3.62)(1+0.8t^2) people per year, where t is the time in years from 1970. The population in 1976 was 726. What was is it in 1984?
I' ve been trying integrating and then evaluating the integral at t=8 (8 years, 1984-1976=8). The answer must be approx. 3195. I want to learn this because I saw the next problems in my textbook are similar to this one. It might be silly, but any help is welcome.
Thank you.

First, notice that t is defined as years since 1970. So 1976 corresponds to t=6, and 1984 to t=14. There is no t=8 here.

Try doing the work again, keeping this in mind. If you need more help, be sure to show us your work and your answer, so we can see what happened. (So far, you showed just enough work to see an error!)

 

[KFS]

First, notice that t is defined as years since 1970. So 1976 corresponds to t=6, and 1984 to t=14. There is no t=8 here.

Try doing the work again, keeping this in mind. If you need more help, be sure to show us your work and your answer, so we can see what happened. (So far, you showed just enough work to see an error!)

Thank you for the help. But I've computed t=6 and I got (approximately) 225+C, but it says that in 1976 there were 726 inhabitants so C=500. Then I compute t=14 with C=500 and I get 3134, not 3195. What am I doing wrong here?