Question

Animal control officers have implemented a 12-month program to eliminate rats in a community. The rate of change of the rat population in this community is given by r(x) = 24x05 - 30x rats per month, x months after the program was introduced. Check: (9) = - 198 R(x) is the rat population x months after the start of the program. R(x) is a specific antiderivative of r(x). Use the fact that nine months after the program was introduced, there were 2,557 rats in this community, to find R(x). Report your value of C below. The value of that makes R(x) a specific antiderivative is your answer. 4 pts

Answer 1

= 24X? Il R(x)= 8 (1) dx 0.5 24 x - 30x ) dal 24 308) dx 312 30 x² + c 2 - 2 3. / 16 1²-15 0 + c hi Given that R(q) = 2,55 16x9 * _ 15 x 9 +C - 15X q + C = 2,557 3/2 2

==> 16x 27 - 15 x81 + C = 2557 -> - 7834C = 2557 * A C = 3340 3 义 Rix) - 16-152 13340