Chapter 6.4, Problem 65E

a.

To determine

To determine that the given equations are approximately equivalent.

Explanation of Solution

Given information :

Given equations are,

  $\begin{array}{l}y\approx 800{\left(0.71\right)}^t\\ y\approx 800{\left(0.9943\right)}^{60t}\\ y\approx 800{\left(0.843\right)}^{2t}\end{array}$

Simplify the given equations we get,

  $\begin{array}{l}y\approx 800{\left(0.71\right)}^t\\ y\approx 800{\left(0.9943\right)}^{60t}=800{\left({0.9943}^{60}\right)}^t\approx 800{\left(0.71\right)}^t\\ y\approx 800{\left(0.843\right)}^{2t}=800{\left({0.843}^2\right)}^t\approx 800{\left(0.71\right)}^t\end{array}$

Hence all are nearly equivalent.

b.

To determine

To describe the information given by each of the given fuctions.

Explanation of Solution

Given information :

Given equations are,

  $\begin{array}{l}y\approx 800{\left(0.71\right)}^t\\ y\approx 800{\left(0.9943\right)}^{60t}\\ y\approx 800{\left(0.843\right)}^{2t}\end{array}$

First equation states that the amount of ibuprofen released after 1 hour of taking dosage is 71%.

Second equation states that the amount of ibuprofen released after 1 minute of taking dosage is 99.43%.

Third equation states that the amount of ibuprofen released after half hour of taking dosage is 84.3%.