Chapter MPS, Problem 8.1MPS

(a)

To determine

To find: The equation to represent the caffeine left after drinking a cup of coffee.

Answer to Problem 8.1MPS

  $95{\left[\frac{7}{8}\right]}^t$

Explanation of Solution

Given:

  $$ A cup of coffee $=95mg$ of caffeine

Elimination of caffeine from average teen in 1 hour $=12.5$ percent

Formula Used:

  $x=95{\left[1-\frac{R}{100}\right]}^t$

Calculation:

Let $x$ be the amount of caffeine left after $t$ hour

Amount of remaining caffeine after time $\text{'}t\text{'}$ from drinking a cup of coffee

  $\begin{array}{l}x=95{\left[1-\frac{R}{100}\right]}^t\\ x=95{\left[1-\frac{12.5}{100}\right]}^t\\ x=95{\left[1-\frac{1}{8}\right]}^t\\ x=95{\left[\frac{7}{8}\right]}^t\end{array}$

Conclusion:

Thus, the caffeine left is $95{\left[\frac{7}{8}\right]}^t$

(b)

To determine

To Draw: The graph of required expression.

Answer to Problem 8.1MPS

  $95{\left[\frac{7}{8}\right]}^t$

Explanation of Solution

Given:

A cup of coffee $=95mg$ of caffeine

Elimination of caffeine from average teen in 1 hour $=12.5$ percent

Formula Used:

  $x=95{\left[1-\frac{R}{100}\right]}^t$

Calculation:

Let $x$ be the amount of caffeine left after $t$ hour

Amount of remaining caffeine after time $\text{'}t\text{'}$ from drinking a cup of coffee

  $\begin{array}{l}x=95{\left[1-\frac{R}{100}\right]}^t\\ x=95{\left[1-\frac{12.5}{100}\right]}^t\\ x=95{\left[1-\frac{1}{8}\right]}^t\\ x=95{\left[\frac{7}{8}\right]}^t\end{array}$

  

Conclusion:

Thus, the graph has drawn.