1. "What interest rate, if compounded continuously, is needed for an investment to double in 7 years?" (I know the formula for interest compounded continuously is Pe^rt but I don't see how I could do this problem with such little information).
2. Find the equation of the tangent line to x^2 + y^2 = 10 at the point (-3,-1).
3. Solve for x: 2^(x-1) = 3^(3-2x) (use the properties of logarithms to simplify your answer)
Any help at all would be much appreciated! Thanks :)
2. Find the equation of the tangent line to x^2 + y^2 = 10 at the point (-3,-1).
3. Solve for x: 2^(x-1) = 3^(3-2x) (use the properties of logarithms to simplify your answer)
Any help at all would be much appreciated! Thanks :)
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1. e^7t = 2
7t = ln(2)
7t = 0.69
t = 0.693 / 7
t = 0.099
Let's check. e^(7 X 0.099) = e^0.693 = 1.9997 (close enough to 2).
I worked in finance for thirty-five years. There's a rule of 72, which says that an investment at any interest rate between 3% and 20% will double in a number of years that is approximately 72 divided by the percentage, so I'd expect a 10% interest rate to double in about 7 years. The reason that it's the rule of 72, rather than the rule of 69, is that most interest is compounded monthly, which means it takes just a bit longer to double. Also, 72 is divisible by more numbers than is 69.
7t = ln(2)
7t = 0.69
t = 0.693 / 7
t = 0.099
Let's check. e^(7 X 0.099) = e^0.693 = 1.9997 (close enough to 2).
I worked in finance for thirty-five years. There's a rule of 72, which says that an investment at any interest rate between 3% and 20% will double in a number of years that is approximately 72 divided by the percentage, so I'd expect a 10% interest rate to double in about 7 years. The reason that it's the rule of 72, rather than the rule of 69, is that most interest is compounded monthly, which means it takes just a bit longer to double. Also, 72 is divisible by more numbers than is 69.
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1) A = Pe^rt
You don't need to know the starting and ending amount just that it double. So lets make one up assume that the initial investment P = $2. Then the final amount would be 4. so A = $4
Either way you get 4 = 2e^rt so dividing by two you get 2 = e^rt we know t = 7.
so
2 = e^r7
we can use the natural log to solve this
2 = e^r7 is the same as ln (2) = 7r so r = (ln(2))/7 which can be found in a calculator.
You don't need to know the starting and ending amount just that it double. So lets make one up assume that the initial investment P = $2. Then the final amount would be 4. so A = $4
Either way you get 4 = 2e^rt so dividing by two you get 2 = e^rt we know t = 7.
so
2 = e^r7
we can use the natural log to solve this
2 = e^r7 is the same as ln (2) = 7r so r = (ln(2))/7 which can be found in a calculator.
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1) 10%.
the rule of 7 says that a 7% interest rate will double your investment in 10 years and that a 10% interest rate will double in 7 years.
the rule of 7 says that a 7% interest rate will double your investment in 10 years and that a 10% interest rate will double in 7 years.