A company is trying to introduce a new product to as many people as possible thr

Question

A company is trying to introduce a new product to as many people as possible through television advertising in a large metropolitan area with 2 million possible viewers. A model for the number of people N (in millions) who are aware of the product after t days of advertising was found to be N = 2(1 - e^-0.032t). Graph this function for 0 lessthanorequalto t lessthanorequalto 50. What value does N tend to as t increases without bound? Choose the correct graph below. What value does N tend to as t increases without bound? A company is trying to introduce a new product to as many people as possible through television advertising in a large metropolitan area with 3 million possible viewers. A model for the number of people N (in millions) who are aware of the product after t days of advertising was found to be N = 3(1 - e^-0.042t). Graph this function for 0 lessthanorequalto t lessthanorequalto 50. What value does N tend to as t increases without bound? Choose the correct grap

Explanation / Answer

Here to get different points for plotting in ordered pair form (x,y), we let some values of x and calculate the function for corresponding value of N

so if let x= 0

then N= 2(1-e^{-0.0032(0)})=2(1-0)=2

so first point is (0,2)

When x= 10

then N= 2(1-e^{-0.0032(10)}= 2(1-e^{-0.032})=2(1-1.03252) = 2(-0.03252) =- 0.0.65

so second point is (10,-0.0.65)

AGain when x=20

then N= 2(1-e^{-0.0032(20)}=N= 2(1-e^{-0.064})=3(1-1.066) = 2(-0.066) = -0.132

so another point is (20,-0.0132).

Again when x=40

then N= 2(1-e^{-0.0032(40)}=2(1-e^{-0.128})=2(1-1.1366)= 2(-0.1366) = -.02732

So another point is (40,-0.2732)

So on plotting these points in XY plane, we get its graph as shown in option D. So its correct answer is option D.

Now by graph it is cleared that as x tends to infinity, N tends to zero,

so required value of N , when x tends to unbound is 0.

This is the answer of first question.

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