Question

A stock broker is evaluating the value of a certain share with each week. The function that describes the value of the share, v, in dollars, after n weeks is given below, where b is an unknown positive base.

v(n) = (14) times b^2

Select the correct statement.

If b = 1.06, the weekly percent growth rate of the share's value is 6%.

If b = 1.8, the weekly percent growth rate of the share's value is 8%.

If b = 0.84, the weekly percent growth rate of the share's value is 84%.

If b = 0.77, the weekly percent growth rate of the share's value is 23%.

Answer 1

A. If b = 1.06, the weekly percent growth rate of the share's value is 6%.

Explanation:

We are given that,

The function representing the value of shares (v) after (n) weeks is given by,

`v(n)=14(b)^2`

According to the question, the value represents an exponential growth.

The general form of an exponential growth is
`a(1+r)^x`, where 'r' is the growth rate.

On comparing, we get that the value
`b=1+r`

Since, b > 1. So, option C and D are not correct.

If b=1.06 i.e. b=1+0.06. Then, the growth rate is r=0.06 or r=6%.

If b=1.8 i.e. b=1+0.8. Then, the growth rate is r=0.8 or r= 8)%.

So, option B is discarded.

Thus, option A is correct.

Answer 2

We have the following equation:
v(n) = 14(b)^n
Where,
n: number of weeks
growth rate means ----> b>1
In this case:
b=1.06 > 1
the correct statement is:
If b = 1.06, the weekly percent growth rate of the share's value is 6%.
Answer:
If b = 1.06, the weekly percent growth rate of the share's value is 6%.