consider the following problem: the population of ants in chloes ant farm changes at a rate of…

consider the following problem: the population of ants in chloes ant farm changes at a rate of r(t)=-15.8·0.9^t ants per month (where t is time in months). at time t = 0, the ant farms population is 150 ants. how many ants are in the farm at t = 4? which expression can we use to solve the problem? choose 1 answer: a 150+∫_0^4 r(t)dt b ∫_3^4 r(t)dt c ∫_0^4 r(t)dt d 150+∫_3^4 r(t)dt

consider the following problem: the population of ants in chloes ant farm changes at a rate of r(t)=-15.8·0.9^t ants per month (where t is time in months). at time t = 0, the ant farms population is 150 ants. how many ants are in the farm at t = 4? which expression can we use to solve the problem? choose 1 answer: a 150+∫_0^4 r(t)dt b ∫_3^4 r(t)dt c ∫_0^4 r(t)dt d 150+∫_3^4 r(t)dt

Answer

Explanation:

Step1: Recall population - change formula

The net - change in a quantity over an interval $[a,b]$ is given by $\int_{a}^{b}r(t)dt$, where $r(t)$ is the rate of change of the quantity with respect to time $t$. The population $P(t)$ at time $t$ can be found using the initial population $P(0)$ and the net - change in population over the interval $[0,t]$. The formula for the population at time $t$ is $P(t)=P(0)+\int_{0}^{t}r(s)ds$.

Step2: Identify given values

We are given that $P(0) = 150$ (the initial population at $t = 0$), $r(t)=- 15.8\cdot0.9^{t}$, and we want to find the population at $t = 4$. Substituting these values into the formula, we get $P(4)=150+\int_{0}^{4}r(t)dt$.

Answer:

A. $150+\int_{0}^{4}r(t)dt$