Chapter 7.8, Problem 13PFA

To determine

To calculate: the true statement about the growth of the bacteria.

Answer to Problem 13PFA

Options B, C and E are correct!

Explanation of Solution

Given information: The function A(t) = 200(1.4)t

Let’s analyze each option.

For option A, t = 20 minutes or $t=\frac{20}{60}$ hours.

Plug in t as $\frac{20}{60}$ into the equation to find A.

  $A(\frac{20}{60})=200{(1.4)}^{\frac{20}{60}}$

  $=223.74$

So, option A is false.

For option B:

Growth factor is 1.4. It means growth rate is $1+r=1.4$

Solve it for ‘ r’

Subtract both sides 1,

  $r=0.4$

Multiply by 100% to get answer in percent.

  $r=0.4*100\%$

  $r=40\%$

Yes! Option B is right.

For option C:

Let’s find growth rate to hour by simplifying ${(1.0056)}^{60}$

  $=\mathrm{1.398...}$

Round to nearest tenth, it is 1.4.

So, this option is too true.

For option D:

To find growth rate per second, let’s divide 40% by 3600 because there are 3600 seconds in 1 hour.

  $\frac{40\%}{3600}=0.011\%approximately$ .

So, this option is false

For option E:

According to the given equation initial population of bacteria is 200.

Conclusion: For this problem options B, C and E are correct!