SOLUTION: A new model BMW convertible coupe is designed and produced in time to appear in North America in the fall. BMW Corporation has a limited number of new models available. The number

Question 1126129: A new model BMW convertible coupe is designed and produced in time to appear in North America in the fall. BMW Corporation has a limited number of new models available. The number of new model BMW convertible coupes purchased in North America is given by N=100,000/1+10e^2t where t is the number of weeks after the BMW is released.
a. How many new model BMW convertible coupes will have been purchased 3 weeks after the new model becomes available? Round your answer to the nearest integer.
b. How many after 35 weeks?
c. What is the maximum number of new model BMW convertible coupes that will be sold in North America?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula is N = 100,000 / (1 + 10 * e ^ (2 * T).

T is the number of weeks after the BMW is released.

there is something wrong with your equation.

as written, i get the following graph.

$$$

when i make 2 * T becomes -2 * T, i get the following graph.

$$$

the second graph is what i would expect to see.

the growth goes up rapidly and then saturates at a maximum level.

i'd go with y = 100,000 / (1 + 10 * e ^ (-2 * T)).

using that formula, you get:

9091 vehicles purchased 3 weeks after launch.

97,581 vehicles purchased 35 weeks after launch.

the sale of vehicles saturates at 100,000 vehicles.

apparently, based on the formula, they expect lots of sales pretty soon after launch but don't expect the total number to get beyond 100,000.

check your formula.

i think you'll find that the exponent is negative (e^-2T rather than e^2T).

note that 1 + 10 * e^-2T is the same as 1 + 10/e^2T.

as T gets larger, 10 / e^2T becomes smaller until it gets very close to 0, at which time 1 + 10/e^2T becomes very close to 1 and 100,000 / (1 + 10/ e^2T) gets very close to 100,000 / 1 = 100,000.

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