16
QuizMultiple Choice

Mathematical Modeling: Part Three — Test

Question 16 • Mathematics III

A factory produces 1 comma 250 comma 000 toys each year. The number of toys is expected to increase by about 150 percent per year. Which model can be used to find the number of toys, n (in millions), being produced in t years?

Answer
A
n is equal to 1 point 2 5 times 2 point 5 to the t th power
B
n is equal to 1 point 5 t plus 1 point 2 5
C
n is equal to the fraction with numerator 2 point 5 times 1 point 5 and denominator t , t is not equal to 0
D
n is equal to 1 point 5 t squared plus 1 point 2 5

Explanation

The factory initially produces 1,250,000 toys, which is 1.25 million, so the model starts with 1.25. An increase of 150% means the amount grows by 1.5 times its current value each year, giving a yearly growth factor of 1 + 1.5 = 2.5. Therefore, after t years the model is n = 1.25(2.5)^t, choice A.

AI-written and checked against the verified answer.

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