how long would it take for the investment to triple using this equation: A=3200e^(0.062t) and would i solve this
To find the time it would take for the investment to triple, we need to solve the equation A = 3200e^(0.062t), where A represents the value of the investment at time t.
To solve this equation, follow these steps:
Step 1: Write down the equation
A = 3200e^(0.062t)
Step 2: Divide both sides of the equation by 3200
A/3200 = e^(0.062t)
Step 3: Take the natural logarithm (ln) of both sides of the equation
ln(A/3200) = ln(e^(0.062t))
Step 4: Simplify the right side of the equation using the property of logarithms (ln(e^x) = x)
ln(A/3200) = 0.062t
Step 5: Divide both sides of the equation by 0.062
(ln(A/3200))/0.062 = t
Step 6: Simplify the left side of the equation by dividing ln(A/3200) by 0.062
t = (ln(A/3200))/0.062
Now that we have the equation t = (ln(A/3200))/0.062, we can plug in the value of A = 3 times the initial investment to find the time it would take for the investment to triple.
Let's assume the initial investment is 3200.
A = 3 * 3200 = 9600
Plug in A = 9600 into the equation:
t = (ln(9600/3200))/0.062
Now, use a calculator to evaluate the right side of the equation to find the value of t.
By following these steps, you can find the time it would take for the investment to triple using the given equation.