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Investment The time required to double the amount of aninvestment at an interest rate $r$ compounded continuously isgiven by$$t=\frac{\ln 2}{r}$$Find the time required to double an investment at $6 \%, 7 \%$and 8$\% .$

6 percent: $t \approx 11.552$7 percent: $t \approx 9.902$8 percent: $t \approx 8.664$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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So to find the time it takes to Dublin in it, an initial investment well, we have to do is plug in our interest rates into the given equation. And so for 6%. So let's say for 6% we have we have t is equal to t is equal to the natural log of to over 6%. We can rewrite this as 60.6 and then for 7% or 7% we have t is equal to the natural log of to over 0.7 and then lastly we have 8%. So then this gives us t is equal to the natural log of two over 20.8 and so So now we can solve for these values. So t is equal to the natural log of two divided by 20.6 This gives us 11.6 years. Then we have we have natural log of two divided by 20.7 This gives us t is equal to 9.9 years and then lastly, we have this 8% interest rate, which is if we plug this in, we get eight point 8.7 years. So these are These are our three solutions

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