7
advanced-math

In the function V(t)=2500(1.08)tV(t) = 2500(1.08)^t, which describes the value of an investment over time, what does the number 1.08 represent?

A

The initial investment was $1.08.

B

The investment grows by $1.08 each year.

C

The investment grows by 8% each year.

D

The investment grows by 108% each year.

Correct Answer: C

Choice C is the correct answer. The base 1.081.08 indicates the percentage growth rate.

  1. Analyze Base: The growth factor is b=1.08b = 1.08.
  2. Find Rate: Since b=1+rb = 1 + r, we have 1.08=1+r1.08 = 1 + r, so r=0.08r = 0.08.
  3. Convert to %: 0.08=8%0.08 = 8\%.

💡 Strategic Tip: To find the percentage rate from the factor 1.XX1.XX, just look at the decimal part XXXX.

Choice A is incorrect because the initial investment is 2500. Choice B is incorrect because exponential growth is by a percentage, not a fixed dollar amount. Choice D is incorrect because 108% growth would mean b=2.08b = 2.08.