Chapter 7.5, Problem 54PPE

a.

To determine

To calculate: After 2 hours, there were $144$ cells in the culture. What was $N$.

Answer to Problem 54PPE

  $N=100$

Explanation of Solution

Given information: The number of cells in a cell culture grows exponentially. The number of cells in the culture as a function of time is given by the expression $N{\left(\frac{6}{5}\right)}^t$ where $t$ is measured in hours and $N$ is the initial size of the culture.

Calculation:

The number of cells in the culture as a function of time is given by the expression $N{\left(\frac{6}{5}\right)}^t$

Where, $t=2$ and number of cells $=144$

  $\therefore 144=N{\left(\frac{6}{5}\right)}^2$

  $\therefore N=100$

b.

To determine

To calculate: How many cells were in the culture after 20 minutes

Answer to Problem 54PPE

number of cells in the culture is $107$

Explanation of Solution

Given information: The number of cells in a cell culture grows exponentially. The number of cells in the culture as a function of time is given by the expression $N{\left(\frac{6}{5}\right)}^t$ where $t$ is measured in hours and $N$ is the initial size of the culture.

Calculation:

There were initially $N=100$ cells,

Now, after 20 minutes, i.e. $t=\frac{1}{3}$ h, number of cells in the culture is,

  $=100{\left(\frac{6}{5}\right)}^{\frac{1}{3}}$

  $=106.26\approx 107$

c.

To determine

To calculate: How many cells were in the culture after 2.5 hours

Answer to Problem 54PPE

number of cells in the culture is $158$

Explanation of Solution

Given information: The number of cells in a cell culture grows exponentially. The number of cells in the culture as a function of time is given by the expression $N{\left(\frac{6}{5}\right)}^t$ where $t$ is measured in hours and $N$ is the initial size of the culture.

Calculation:

There were initially $N=100$ cells,

Now, after 2.5 hours, i.e. $t=2.5$ h, number of cells in the culture is,

  $=100{\left(\frac{6}{5}\right)}^{2.5}$

  $=157.75\approx 158$