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

Answer:

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

Step-by-step 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%.