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What interest rate compounded continuously did a $\$ 15,000$ investment earn if it accumulated to $\$ 18,000$ in 5 years?

$$3.65 \%$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

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Harvey Mudd College

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Okay, I see that phrase compounded continuously again. So that's telling me to use perc formula p e to the R T. So as you break down everything that's given to you, we we want to end with 18,000. If we start with 15,000, we don't know the rate. That's what we're trying to find. Remember is just a number, by the way, he's always the same number on they tell you in five years. So after five years s So we have to find that interest rates always the same steps. By the way, you want to divide the principal over that way. It's just an exponential function. And by the way, you can reduce what you don't have to, you know, divide both top and bottom by 1000. You have 18/15. Uh, you could divide both those by three. Aziz. Well, so you have six fists? Yeah. Um Thio Undo e u natural log. It's the inverse operation of E. The reason why this works is what you're technically doing is is you're creating the exponents a way to move it to be multiplication moving in front, natural. You'll be is just one So we're looking at five R is equal to that. And again, it's a multiplication problem. So to solve that you divide. Now I remember this gives you the rate as a decibel eso as you type that into your calculator. Six fists, all divided by five. You get 50.364643114 But when we want the rate, we want it as a percent. So we gotta move that decimal over twice. So we're looking at 3.646%. I liked around the three decimals. By the way, um, you might round it differently. I don't know. Yeah.

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