Answer
a. The value of the derivative $P'(5)$ indicates the number of yeast cells that the culture will grow by at the time, $t=5$. The units are cells/second.
b. By observing the graphs, sketching a tangent at both values of $t=2$ and $t=3$, the slope at $t=3$ will be greater indicating a greater growth rate of yeast cells.
c. To find the instantaneous rate of growth at the time of 5 hours, we need to find the derivative function of the population function.
Given that $P(t)=6.10t^2 - 9.28t + 16.43$
then, $P'(t)=2(6.10)t^{2-1}-9.28t^{1-1}=12.20t-9.28$
Thus, $P'(5)=12.20(5)-9.28=51.72$ cells per second
Work Step by Step
a. The value of the derivative $P'(5)$ indicates the number of yeast cells that the culture will grow by at the time, $t=5$. The units are cells/second
b. By observing the graphs, sketching a tangent at both values of $t=2$ and $t=3$, the slope at $t=3$ will be greater indicating a greater growth rate of yeast cells.
c. To find the instantaneous rate of growth at the time of 5 hours, we need to find the derivative function of the population function.
Given that $P(t)=6.10t^2 - 9.28t + 16.43$
then, $P'(t)=2(6.10)t^{2-1}-9.28t^{1-1}=12.20t-9.28$
Thus, $P'(5)=12.20(5)-9.28=51.72$ cells per second
