1
advanced-math

Consider the function f(x)=80(0.75)xf(x) = 80(0.75)^x. What are the initial value and the growth/decay factor?

A

Initial value: 80, Factor: 0.75 (Growth)

B

Initial value: 80, Factor: 0.75 (Decay)

C

Initial value: 0.75, Factor: 80 (Growth)

D

Initial value: 80, Factor: 0.25 (Decay)

Correct Answer: B

Choice B is the correct answer. Identify components in y=abxy=ab^x.

  1. Identify a: The coefficient is 80, so the initial value is 80.
  2. Identify b: The base is 0.75.
  3. Classify: Since 0<0.75<10 < 0.75 < 1, it represents decay.

💡 Strategic Tip: A decimal base like 0.75 means you are keeping 75% of the value, so it's shrinking.

Choice A is incorrect because 0.75 implies decay, not growth. Choice C is incorrect because it swaps aa and bb. Choice D is incorrect because 0.25 is the decay rate (25%), not the factor.