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What interest rate compounded continuously did a $\$ 275$ investment earn if it accumulated to $\$ 540$ in 12 years?

$$5.62 \%$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

Baylor University

Idaho State University

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All right. This is a classic hurt problem. P e to the r t. We're piece dancer principle. Well, as you look at the problem Mm. The principles. $275. Uh, he is just a number we're solving for the rate and then the tea. And the problem is 12 years for you to accumulate to $540. Eso It's just a bunch of inverse operations. The first thing to do would be to divide 275 over. So those two pieces of cancel now toe undo E you take the natural log on both sides. You can probably guess I'm going to go to a calculator soon. So that cancels out this in the very last step is to divide both sides by 12. Because you're left with 12 r equals, whatever this number is over here. So to solve the multiplication problems to divide. So as you do that I'm just typing into my calculator because nobody, I don't think anybody would expect you to do this math in your head. Especially since he is an irrational number all over 12. Now, remember, they give you the answer as a decimal. But the rate, um, there's two different ways you can do it. Just you multiplied by 100 or quickly just move that decimal over twice to figure out the interest rate is 5.6. I liked around three decimal places. Uh, depending on your teacher, how he or she wants you to write it 5.6 to 3%.

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