Question

A survey reveals that the sales of smartphones is increasing considerably. The average annual sales of smartphones, in million units, n years after the survey is conducted is modeled by function p below. The parameter b is an unknown positive base.

Answer 1

Answer:

C. When the survey was initially conducted average sales of smartphones was 1.7 millions units.

Step-by-step explanation:

We have been given that the average annual sales of smartphones, in million units, n years after the survey is conducted is modeled by function $p(n)=1.7\cdot b^n$, where the parameter b is an unknown positive base.

We are asked to find the true statement about our given function.

A. If b= 1.45, the annual growth rate of the sales of smartphones is 145%.

Since we know that b equals (1+r) for growth function, where r is in decimal form.

If b=1.45, it means that the annual growth rate will be 45% as 0.45 is decimal form of 45%, therefore, statement A is not true.

B.  If b= 1.02, annual sales of smartphones will double in 2 years.

If b=1.02, it means that the annual growth rate will be 2% as 0.02 is decimal form of 2%, therefore, statement B is not true.

C. When the survey was initially conducted average sales of smartphones was 1.7 millions units.

Since we know that an exponential function is in form $y=a*b^x$, where a in initial value of function. We can see from our given function that a equals 1.7, therefore option C is a true statement.

D. The average sales of smartphones increases by 1.7 millions units every year.

Since our function is not a linear function, instead it is an exponential function, so rate of change can not be constant.

Therefore, option D is not true regarding our given function.