The population of aphids on a rose plant increases at a rate proportional to the number present.In 5 days the population grew from 700 to 1100.Which of the following formulas give for the population of aphids at time t in days, where t = 0 is the day when there were 700 aphids?
A) $P=700 e^{5 t}$
B) $P=700 e^{\left(\frac{1}{5} \ln \frac{11}{7}\right) t}$
C) $P=700 e^{2000 t}$
D) $P=700 e^{\left(\frac{1}{5} \ln 400\right) t}$

Question

Quizplus · Accepted Answer

The population growth is exponential, and the formula for exponential growth is $P = P_0 e^{rt}$, where $P_0$ is the initial population, $r$ is the rate of growth, and $t$ is time. Given that the population grows from 700 to 1100 in 5 days, we can use these values to solve for $r$. The correct formula that represents this situation is $P=700 e^{\left(\frac{1}{5} \ln \frac{11}{7}\right) t}$, which correctly applies the exponential growth formula with the given increase in population over the specified time period.

The Population of Aphids on a Rose Plant Increases at a Rate