Question

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

\\(n = \frac{2.5(1.5)}{t}, t \
eq 0\\)

\\(n = 1.5t^2 + 1.25\\)

\\(n = 1.5t + 1.25\\)

\\(n = 1.25 \cdot 2.5^t\\)

Explanation:

Identify the initial value in millions

$$ a = \frac{1,250,000}{1,000,000} = 1.25 $$

Determine the growth factor

$$ b = 1 + r = 1 + 1.50 = 2.5 $$

Formulate the exponential model

$$ n = a \cdot b^t = 1.25 \cdot 2.5^t $$

Answer:

• (A) \(n = \frac{2.5(1.5)}{t}, t

eq 0\)

• (B) \(n = 1.5t^2 + 1.25\)
• (C) \(n = 1.5t + 1.25\)
• (D) \(n = 1.25 \cdot 2.5^t\) (Correct answer)