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What interest rate compounded continuously did a $\$ 1000$ investment earn if it accumulated to $\$ 1250$ in 3 years?

$$7.44 \%$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

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the moment you see that phrase continuously, you need to think of the perp formula. P E to the R T is equal to your ending balance. And c they tell you were starting with 1000. We don't know the rate, but they do tell you in three years. So our times three or three are If you want to write it this way is equal to 12 50. That's the ending balance. So to solve this problem, it's the same steps over and over again. You divide 1000 over and you can reduce that if you want. You know, dividing both sides by 10 and you could divide both sides by 25 even to make that equal to five force. You don't have to. But then your next step is to get rid of E What you take the natural log of both sides s. So what we're left with is is because we took the log of both sides. Really? This are times three gets moved in front and natural. Aga B is one eso then from here to find your interest rate, you just gotta divided by three. Uh, now that gives you the R value as a decimal earth. Yeah, as a desperate. So I'm just typing in natural of the five force divided by three, I get a decimal of 0.7438 118 Um, but the questions asking for the rate, not just the r value. So you gotta move that decimal back over. Um, someone can approximate 7.438%. That's the answer we're looking for. So hopefully all that made sense.

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