Question

the quarterly revenue of a social media app (in millions of dollars) from 2017 through 2022 can be modeled by the exponential function f(x) = 7.900(2.935)^x, where x = 0 represents the first quarter of 2017, x = 1 represents the first quarter of 2018, and so on. use this model to approximate the revenue for the app in the first quarter of each year, to the nearest million. (a) 2017 (b) 2020 (c) 2022 (a) the first quarter revenue for 2017 was approximately 8 million. (round to the nearest integer as needed.) (b) the first quarter revenue for 2020 was approximately 200 million. (round to the nearest integer as needed.) (c) the first quarter revenue for 2022 was approximately 1912 million. (round to the nearest integer as needed.)

Explanation:

Step1: Find the value of \(x\) for each year

• For 2017: \(x = 0\)
• For 2020: \(x=2020 - 2017=3\)
• For 2022: \(x = 2022-2017 = 5\)

Step2: Substitute \(x\) into the function \(f(x)=7.900(2.935)^{x}\)

• For 2017 (\(x = 0\)):

$$
LATEXBLOCK0
$$

• For 2020 (\(x = 3\)):

$$
LATEXBLOCK1
$$

• For 2022 (\(x = 5\)):

$$
LATEXBLOCK2
$$

Answer:

(a) \(8\) million.
(b) \(200\) million.
(c) \(1912\) million.