Chapter 6.4, Problem 40E

a.

To determine

To find: whether the function that is represented by the table is exponential growth function, exponential decay function or neither.

Answer to Problem 40E

Exponential Growth Function

Explanation of Solution

Given information:

The table:

t	42	43	44	45
Visitors	11,000	12,100	13,310	14,641

Concept Used:

Exponential growth function:

  $y=a{\left(1+r\right)}^t$

Here, the y is the final value, a is the initial value, and r is the rate of growth (in decimal form).

Exponential decay function:

  $y=a{\left(1-r\right)}^t$

Here, the y is the final value, a is the initial value, and r is the rate of decay (in decimal form).

Consider the table given below:

  

It can be observed that as t increases by 1, the value (visitors) is multiplied by $1.1$ .

So, the function represented by the given table is exponential growth function.

b.

To determine

To find: the number of visitors after website is online for 47 days.

Answer to Problem 40E

Approximately $17,716$

Explanation of Solution

From part (a), it is observed that as t increases by 1, the y -value is multiplied by $1.1$ .

So, as t increase from $t=45$ to $t=47$ that is by t is increased by 1 two times.

The value $v\left(47\right)$ is obtained by multiplying $v\left(45\right)$ by 1.1 two times.

So,

  $\begin{array}{c}v\left(47\right)=14641\times 1.1\times 1.1\\ =17,715.61\end{array}$

Conclusion:

So, number of visitors after website is online for 47 days will be about 17,716.