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.

Question

Which statement is true about this situation?

A.
The average annual sales of smartphones increases by 1.7 million units every year.
B.
If b = 1.45, the annual growth rate of the sales of smartphones is 145%.
C.
If b = 1.02, the annual sales of smartphones will double in 2 years.
D.
When the survey was initially conducted, the average sales of smartphones was 1.7 million units.

Answer 1

To evaluate the statements, we should consider the characteristics of the function \( p(n) \) which models the average annual sales of smartphones over \( n \) years. Since the exact form of \( p(n) \) is not provided, we can analyze the statements based on general knowledge of exponential growth and the meanings of the parameters.

A. The average annual sales of smartphones increases by 1.7 million units every year.

• This statement suggests a linear growth which is typically not the case with exponential models. In exponential growth, the increase is proportional to the current value, not a fixed amount. Therefore, this statement is likely false.

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

• An exponential growth base \( b \) represents the factor by which the quantity grows each year. A base \( b = 1.45 \) implies the sales are increasing by 45% each year (not 145%). Therefore, this statement is false.

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

• With a base of \( b = 1.02 \), the sales will grow by 2% each year. Using the rule of 70 (i.e., doubling time ≈ 70 divided by growth rate), the doubling time for a growth rate of 2% is approximately 35 years, not 2. Therefore, this statement is false.

D. When the survey was initially conducted, the average sales of smartphones was 1.7 million units.

• This statement would depend on the specific model \( p(0) \). If \( p(n) \) is given in such a way that \( p(0) = 1.7 \), then this statement could be true. However, without explicit confirmation of the initial value at the time of the survey, we cannot determine if this statement is true or false based solely on the information given.

Based on the evaluations above, all the statements are found to be false, except for statement D, which could potentially be true depending on the provided model and context. However, without explicit information confirming the initial average sales, it cannot be definitively stated as true. Thus, none of the statements are conclusively true as described without additional context.