Chapter MPS, Problem 8.2MPS

(a)

To determine

To find: The equation to show the number of bacteria as time passes.

Answer to Problem 8.2MPS

  $x=250{\left[\frac{523}{500}\right]}^t$

Explanation of Solution

Given:

Growing rate of bacteria = $4.6$ percent per day.

Number of bacteria at the starting = $250$

Formula Used:

  $x=p{\left[1+\frac{R}{100}\right]}^t$

Calculation:

Let $\text{'}t\text{'}$ be time and $\text{'}x\text{'}$ be the amount of bacteria after time $\text{'}t\text{'}$ and $R$ be the rate percent.

Number of bacteria as time passes

  $\begin{array}{l}x=250{\left[1+\frac{R}{100}\right]}^t\\ x=250{\left[1+\frac{4.6}{100}\right]}^t\\ x=250{\left[1+\frac{23}{500}\right]}^t\\ x=250{\left[\frac{523}{500}\right]}^t\end{array}$

Conclusion:

Thus, the required equation is $x=250{\left[\frac{523}{500}\right]}^t$

(b)

To determine

To Draw: The graph of given expression.

Answer to Problem 8.2MPS

Explanation of Solution

Given:

Growing rate of bacteria = $4.6$ percent per day.

Number of bacteria at the starting = $250$

Formula Used:

  $x=250{\left[\frac{523}{500}\right]}^t$

Calculation:

Let $\text{'}t\text{'}$ be time and $\text{'}x\text{'}$ be the amount of bacteria after time $\text{'}t\text{'}$ and $R$ be the rate percent.

Number of bacteria as time passes

  $\begin{array}{l}x=250{\left[1+\frac{R}{100}\right]}^t\\ x=250{\left[1+\frac{4.6}{100}\right]}^t\\ x=250{\left[1+\frac{23}{500}\right]}^t\\ x=250{\left[\frac{523}{500}\right]}^t\end{array}$

  

Conclusion:

Thus, the required graph has grown.