Question

ginny is studying a population of frogs. she determines that the population is decreasing at an average rate of 3% per year. when she began her study, the frog population was estimated at 1,200. which function represents the frog population after x years?

\\(f(x) = 1,200(1.03)^x\\)
\\(f(x) = 1,200(0.03)^x\\)
\\(f(x) = 1,200(0.97)^x\\)
\\(f(x) = 1,200(0.97x)\\)

Explanation:

Identify the initial value and decay rate

$$
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$$

Determine the decay factor

$$ b = 1 - r = 1 - 0.03 = 0.97 $$

Formulate the exponential function

$$ f(x) = 1200(0.97)^x $$

Answer:

• \(f(x) = 1,200(1.03)^x\)
• \(f(x) = 1,200(0.03)^x\)
• \(f(x) = 1,200(0.97)^x\) (Correct answer)
• \(f(x) = 1,200(0.97x)\)