Chapter 1.4, Problem 10CFU

a.

To determine

To find: equation for length of plant y after x days.

Answer to Problem 10CFU

  $y=5.9x+2$

Explanation of Solution

Given information:

  $\begin{array}{l}x=\text{ days}\\ y=\text{ length}\\ \text{Rate}=5.9\frac{inches}{day}\\ \text{Starting length}=2inches\end{array}$

Calculation

The length can be calculated as follows:

  $\text{Length}=\left(\text{rate}\times \text{days}\right)+\text{Starting length}$

Substitute the known variables and values in the above equation are as follows:

  $\begin{array}{l}y=\left(5.9\frac{inches}{days}\right)x+\text{2}inches\\ y=5.9x+2\end{array}$

Thus, the equation of the line is $y=5.9x+2$ .

b.

To determine

To find: how long the plant grows in one week if it is not cut again.

Answer to Problem 10CFU

  $y=43.3\text{ inches}$

Explanation of Solution

Given information:

  $x=1\text{ week}=7\text{ days}$

  $y=5.9x+2$

Calculation

Put the value of x in the above equation and simply it as follows:

  $\begin{array}{c}y=5.9\left(7\right)+2\\ =41.3+2\\ =43.3\text{ inches}\end{array}$

Thus, the plant grows 43.3 inches.

c.

To determine

To find: and explain can the rate of growth be maintained indefinitely.

Answer to Problem 10CFU

No

Explanation of Solution

Given information: $y=5.9x+2$

Calculation This rate cannot be maintained indefinitely. This equation has real life application, so it does not exist in vacuum. There are additional variables the equation does not account for. And this equation has limit not provided by the question. If we know how long a particular grass is capable of growing, we could determine the number of days for which this is valid.