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Multiple choice📘 F.LE.A.5🧠 DOK 2

Question:

The population of a small town was 5,000 people in 2010 and grew to 6,500 people by 2015. Assuming the population growth follows an exponential model, what is the annual growth rate, expressed as a percentage, of the town's population?

Answer Choices:

A) A) 5%
B) B) 6%
C) C) 7%
D) D) 8%

✅ Answer:

A) 5%

💡 Explanation:

To find the annual growth rate of an exponential function, we use the formula for exponential growth: $P(t) = P_0(1 + r)^t$ .
Here, $P_0$ is the initial population, $P(t)$ is the population at time $t$ , $r$ is the growth rate, and $t$ is the time in years.
Substituting the values, we have $6500 = 5000(1 + r)^5$ .
Solving for $r$ , we get $1.3 = (1 + r)^5$ .
Taking the fifth root of both sides gives $1 + r = 1.053$ , so $r = 0.053$ or 5.3%.
Rounding to the nearest percentage gives a growth rate of 5%.

Standard: F.LE.A.5 | DOK: 2

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