The population of a culture of bacteria has a growth rate given by $$ \mathrm{p}^{\prime}(\mathrm{t})=\frac{230}{(\mathrm{t}+1)^{r}} $$ bacteria per hour, for $$ \mathrm{t} \geq 0 $$, where $$ \mathrm{r}1 $$ is a real number. The increase in the population over the time interval $$ [0, t] $$ is given by $$ \int_{0}^{t} \mathrm{p}^{\prime}(\mathrm{s}) \mathrm{ds} $$. (Note that the growth rate decreases in time, reflecting the competition for food and space.) Complete steps (a) through (e) below. a. Using the population model with $$ \mathrm{r}=2 $$, what is the increase in the population over the time interval $$ 0 \leq t \leq 2 $$ ? The increase in the population over the given interval is approximately $$ \square $$ bacteria. (Round down to the nearest integer as needed.)

Question

The population of a culture of bacteria has a growth rate given by $$ \mathrm{p}^{\prime}(\mathrm{t})=\frac{230}{(\mathrm{t}+1)^{r}} $$ bacteria per hour, for $$ \mathrm{t} \geq 0 $$, where $$ \mathrm{r}>1 $$ is a real number. The increase in the population over the time interval $$ [0, t] $$ is given by $$ \int_{0}^{t} \mathrm{p}^{\prime}(\mathrm{s}) \mathrm{ds} $$. (Note that the growth rate decreases in time, reflecting the competition for food and space.) Complete steps (a) through (e) below. a. Using the population model with $$ \mathrm{r}=2 $$, what is the increase in the population over the time interval $$ 0 \leq t \leq 2 $$ ? The increase in the population over the given interval is approximately $$ \square $$ bacteria. (Round down to the nearest integer as needed.)

Tran Patel · Accepted Answer

The increase in the population over the time interval $$ 0 \leq t \leq 2 $$ with $$ r = 2 $$ is approximately $$ 153 $$ bacteria.

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