the given function f models the number of advertisements a company sent to its clients each year, where x…

the given function f models the number of advertisements a company sent to its clients each year, where x represents the number of years since 1997, and 0 ≤ x ≤ 5. if y = f(x) is graphed in the xy - plane, which of the following is the best interpretation of the y - intercept of the graph in this context? a. the minimum estimated number of advertisements the company sent to its clients during the 5 years was 1,708. b. the minimum estimated number of advertisements the company sent to its clients during the 5 years was 9,000. c. the estimated number of advertisements the company sent to its clients in 1997 was 1,708. d. the estimated number of advertisements the company sent to its clients in 1997 was 9,000.

the given function f models the number of advertisements a company sent to its clients each year, where x represents the number of years since 1997, and 0 ≤ x ≤ 5. if y = f(x) is graphed in the xy - plane, which of the following is the best interpretation of the y - intercept of the graph in this context? a. the minimum estimated number of advertisements the company sent to its clients during the 5 years was 1,708. b. the minimum estimated number of advertisements the company sent to its clients during the 5 years was 9,000. c. the estimated number of advertisements the company sent to its clients in 1997 was 1,708. d. the estimated number of advertisements the company sent to its clients in 1997 was 9,000.

Answer

Explanation:

Step1: Recall the concept of y - intercept

The y - intercept of a function (y = f(x)) is the value of (y) when (x = 0). For the exponential - decay function (f(x)=9000(0.66)^{x}), when (x = 0), we use the property (a^{0}=1) for (a\neq0).

Step2: Calculate the y - intercept

Substitute (x = 0) into the function (f(x)=9000(0.66)^{x}). We get (f(0)=9000(0.66)^{0}). Since ((0.66)^{0}=1), then (f(0)=9000). In the context of the problem, (x) represents the number of years since 1997 and (y = f(x)) represents the number of advertisements. When (x = 0) (the year 1997), the number of advertisements is 9000.

Answer:

A. The minimum estimated number of advertisements the company sent to its clients in 1997 was 9,000.