Chapter 6.1, Problem 51E

(a)

To determine

To identify the decay factor and the percent decrease.

Answer to Problem 51E

The decay factor is $0.9978$ and the decay percentage is $0.22$ .

Explanation of Solution

Given:

The number of eggs $\mathrm{E}$ are modeled by the equation $\mathrm{E}=179.2{(0.89)}^{\frac{\mathrm{w}}{52}}$ where, $\mathrm{w}$ is the number of weeks.

Calculation:

The decay factor is ${(0.89)}^{\frac{1}{52}}=0.9978$

And the decay percentage is $0.22$

(b)

To determine

To graph the model.

Explanation of Solution

Given:

The given graph is V shaped.

Calculation:

The following is the graph of the model-

  

(c)

To determine

To estimate the egg production of a chicken that is $2.5$ years old.

Answer to Problem 51E

  $134\text{ eggs per day}$

Explanation of Solution

Given:

The number of eggs $\mathrm{E}$ are modeled by the equation $\mathrm{E}=179.2{(0.89)}^{\frac{\mathrm{w}}{52}}$ where, $\mathrm{w}$ is the number of weeks.

Calculation:

The equation can be written as follows-

  $\mathrm{E}=179.2{(0.89)}^{\mathrm{y}}$ , where, $\mathrm{y}$ is the number of years.

Therefore the egg production of a chicken that is $2.5$ years old is-

  $\begin{array}{l}$ E=179.2{(0.89)}^y$$ E=179.2{(0.89)}^{2.5}$\mathrm{E}=134\text{ eggs per day}\end{array}$

(d)

To determine

To rewrite the given equation, so that the time is measured in years rather than in weeks.

Answer to Problem 51E

  $\mathrm{E}=179.2{(0.89)}^{\mathrm{y}}$

Explanation of Solution

Given:

The number of eggs $\mathrm{E}$ are modeled by the equation $\mathrm{E}=179.2{(0.89)}^{\frac{\mathrm{w}}{52}}$ where, $\mathrm{w}$ is the number of weeks.

Calculation:

The equation can be written asfollows-

  $\mathrm{E}=179.2{(0.89)}^{\mathrm{y}}$ , where, $\mathrm{y}$ is the number of years.