SOLUTION: The monthly income I, in dollars, from a new product is given by I(t) = 86000 − 65000e^−0.003t where t is the time, in months, since the product was first put on the

Question 1081002: The monthly income I, in dollars, from a new product is given by
I(t) = 86000 − 65000e^−0.003t
where t is the time, in months, since the product was first put on the market. (Round your answers to the nearest dollar amount.)
(a) What was the monthly income after the 50th month and after the 100th month?
I(50) = $
I(100) = $

(b) What will the monthly income from the product approach as the time increases without bound?
$
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula is:

i(t) = 86000 - 65000 * e^-.003t

since e^-a = 1/e^a, this formula becomes:

i(t) = 86000 - 65000 / e^.003t

you can see that, as t gets extraordinarily large, the value of i(t) gets closer and closer to 86000, because the value of 65000 / e^.003t gets closer and closer to zero.

to find the income in the 50th and 100th month, just replace t with 50 and 100 respectively to get:

when t = 50, monthly income = 86000 - 65000 / e^.003*50 = 30053.98153

when t = 60, monthly income = 86000 - 65000 / e^.003*100 = 37846.81566

this can be shown graphically below:

$$$

as t approaches a higher and higher number, the value of y approaches 8600 as shown in the following graph:
$$$

RELATED QUESTIONS
Can you please help... The monthly income I, in dollars, from a new product is given by (answered by checkley77)

For income x (in dollars), a particular state's income tax T (in dollars) is given by... (answered by Fombitz)

Newton's Law of Cooling governs the temperature of an object T(t)T(t) initially at... (answered by jorel1380)

The coordinate of a particle in meters is given by x(t) = 16t − 3.0t 3, where the... (answered by Alan3354,ikleyn)

2. [6 pts.] The gross domestic product (GDP) of a developing country from 1999 (t=0) to... (answered by stanbon)

A particle moves in a straight line so that its distance, s m, from a fixed point A on... (answered by Alan3354)

A particle moves in a straight line so that its distance, s m, from a fixed point A on... (answered by Fombitz)

A body subject to air resistance is allowed to fall from the top of a 36 m tower. Given... (answered by Alan3354)

The number of bacteria in a refrigerated food product is given by N(T)=23T^2 -81 T+50, 3... (answered by solver91311)

SOLUTION: The monthly income I, in dollars, from a new product is given by I(t) = 86000 &#8722; 65000e^&#8722;0.003t where t is the time, in months, since the product was first put on the

SOLUTION: The monthly income I, in dollars, from a new product is given by I(t) = 86000 − 65000e^−0.003t where t is the time, in months, since the product was first put on the