How do i work this problem out using the equation a=pe^rt

$177.38

Step-by-step explanation:

The first thing you want to do is figure out your variables. In A = Pe^(rt), "A" is the end amount (AKA however much money you have after however much time), "P" is the principle amount (AKA however much you have to start with), "r" is the rate, and "t" is the time. Take all the information they gave you in the problem and try to place it in one of these categories.

Tyler opened a savings account 6 years ago. Ding-ding, we've got a time. The account earns 2% interest, compounded annually. There's our rate. If the current balance is $200.00, how much did he deposit initially?

So, sort these out. t = 6 years. r = 2%, or r = .02. The current balance is $200.00, so is this your end amount or the money you had to start with? Well, since the question is asking you to find how much Tyler deposited initially, you know for sure $200.00 is your end amount ("A"). Let's find out what he started with.

200 = Pe^(.02)(6)

Note that e is not a variable, but a value. You won't ever replace it; it's part of your formula. What you want to solve for here is "P" to get your starting amount. Divide both sides by e^(.02)(6), and you'll see:

P = 200/[e^(.02)(6)] = 177.3840873

Since we're talking money, round that to the nearest cent like your question asked, and you get $177.38. You can check your answer by plugging this value back into A = Pe^(rt) with $177.38 being the principle amount. You get $200 back, so the answer is correct.