2
advanced-math

A savings account grows according to A(t)=5000(1.04)tA(t) = 5000(1.04)^t. What is the balance after 0 years?

A

$5000

B

$5200

C

$1.04

D

$0

Correct Answer: A

Choice A is the correct answer. Substitute t=0t = 0.

  1. Substitute: A(0)=5000(1.04)0=5000(1)=5000A(0) = 5000(1.04)^0 = 5000(1) = 5000.
  2. Initial Deposit: The balance at t=0t=0 is the initial amount deposited.

💡 Strategic Tip: For y=abxy = ab^x, when x=0x=0, the result is always aa (the initial value).

Choice B is incorrect because this is the balance after 1 year, not 0 years. Choice C is incorrect because 1.04 is the growth factor, not a dollar amount. Choice D is incorrect because there is an initial deposit.