Question

the population of a town of 7,000 increases by 5% every year over the next 4 years. if the domain of \\{0, 1, 2, 3, 4\\} for this situation represents the years that the towns population was recorded, what is the range of the population values?

a. \\{7350, 7718, 8103, 8509, 8934\\}
b. \\{7000, 7350, 7718, 8103, 8509\\}
c. \\{7000, 10500, 15750, 23625, 35438\\}
d. \\{7000, 7350, 8103, 8509, 8934\\}

Explanation:

Define the exponential growth model

Using the Exponential Growth knowledge point

$$ P(t) = P_0(1 + r)^t $$

where \(P_0 = 7000\) and \(r = 0.05\).

Calculate population values for the domain

Using the Exponential Growth knowledge point

$$
LATEXBLOCK0
$$

Determine the range set

Using the Exponential Growth knowledge point

$$ \text{Range} = \{7000, 7350, 7718, 8103, 8509\} $$

Answer:

• A. \(\{7350, 7718, 8103, 8509, 8934\}\)
• B. \(\{7000, 7350, 7718, 8103, 8509\}\) (Correct answer)
• C. \(\{7000, 10500, 15750, 23625, 35438\}\)
• D. \(\{7000, 7350, 8103, 8509, 8934\}\)