an automobile company is ready to introduce a new line of cars through a national sales campaign. after test…

an automobile company is ready to introduce a new line of cars through a national sales campaign. after test marketing the line in a carefully selected city, the marketing research department estimates that the sales (in millions of dollars) will increase at the monthly rate of the following function for t months after the campaign has started. s(t)=15 - 13e^{-0.1t} 0≤t≤20 (a) what will be the total sales, s(t), t months after the beginning of the national sales campaign if we assume no sales at the beginning of the campaign? s(t)=15t + 130e^{-0.1t} - 130 (b) what are the estimated total sales for the first 10 months of the campaign? □ million (round to the nearest whole number.)

an automobile company is ready to introduce a new line of cars through a national sales campaign. after test marketing the line in a carefully selected city, the marketing research department estimates that the sales (in millions of dollars) will increase at the monthly rate of the following function for t months after the campaign has started. s(t)=15 - 13e^{-0.1t} 0≤t≤20 (a) what will be the total sales, s(t), t months after the beginning of the national sales campaign if we assume no sales at the beginning of the campaign? s(t)=15t + 130e^{-0.1t} - 130 (b) what are the estimated total sales for the first 10 months of the campaign? □ million (round to the nearest whole number.)

Answer

Explanation:

Step1: Substitute ( t = 10 ) into ( S(t) )

Given ( S(t)=15t + 130e^{-0.1t}-130 ), when ( t = 10 ), we have ( S(10)=15\times10+130e^{-0.1\times10}-130 ). First, calculate ( 15\times10 = 150 ) and ( - 0.1\times10=-1 ), so ( S(10)=150+130e^{-1}-130 ). Simplify ( 150 - 130=20 ), then ( S(10)=20 + 130e^{-1} ). Since ( e^{-1}=\frac{1}{e}\approx0.3679 ), then ( 130e^{-1}=130\times0.3679 = 47.827 ). So ( S(10)=20 + 47.827=67.827 ).

Step2: Round the result

Rounding ( 67.827 ) to the nearest whole number. Since the decimal part ( 0.827>0.5 ), we round up.

Answer:

( 68 ) million.