Chapter 7.5, Problem 7CYU

a.

To determine

To calculate the domain and range of the function

Answer to Problem 7CYU

Domain: $(-\infty ,\infty )$

Range: $(0,\infty )$ for all y, $y>0$

Explanation of Solution

Given:

Function: $f(t)=100{(1.05)}^t$ where $f(t)$ is the number of flies and $t$ is the time in days.

Calculation for graph:

Consider $y=100{(1.05)}^t$

Values of x	Values of y
0	100
1	105
2	110.25
-1	95.23

By taking different values of x , the graph can be plotted.

Graph:

  

Interpretation:

Domain:

The domain of the expression $f(t)=100{(1.05)}^t$ is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Hence,

Domain: $(-\infty ,\infty )$

Range is the set of all y -values that the function passes through.

Hence,

Range: $(0,\infty )$ for all y, $y>0$

b.

To determine

To calculate the population of the fruit fly after 2 weeks.

Answer to Problem 7CYU

198

Explanation of Solution

Given:

Function: $f(t)=100{(1.05)}^t$ where $f(t)$ is the number of flies and $t$ is the time in days.

  $\begin{array}{l}t=2\text{ weeks}\\ \Rightarrow t=14[\because 1\text{ week}=\text{7]}\end{array}$

Calculation:

Given that the function represents the growth of fruit flies.

  $f(t)=100{(1.05)}^t$

Substitute the value of $t$ in the function

  $\begin{array}{l}$ \Rightarrow f(t)=100{(1.05)}^{14}$\Rightarrow f(t)=100(1.9799)\\ \Rightarrow f(t)=197.99\simeq 198\end{array}$

Conclusion:

After two weeks the population of the fruit flies will be 198.