Exponential Growth Calculator

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You start with an initial value of 1200

This accumulates to exponentially to 2400 at a rate of 0.105

How long did this take?:

Since r = 0.105 > 0, we have an exponential growth equation

The exponential growth equation is as follows:

Pe^rt = A where P is your initial starting value, r is your rate,and t is time it takes to grow your initial investment/amount to A, your final value.Note: e is Eulers Constant = 2.718281828459

Plugging in our known values, we get:

1200e^0.105t = 2400

Step 1: Divide each side of the equation by 1200 to isolate (t):

Step 2: Cancel the 1200 on the left side:

e^0.105t = 2

Step 3: Take the natural log Ln of both sides of the equation to remove e:

Ln(e^0.105t) = Ln(2)

There exists a logarithmic identity which states: Ln(eⁿ) = n, so we have

0.105t = 0.69314718055995

Step 4: Divide each side of the equation by 0.105 to isolate (t):

Step 5: Cancelling 0.105 on the left side of the equation and simplifying the right, we can solve for (t):

t = 6.6014017196185

Summary:

Final Answer:

Therefore, it would take 6.6014017196185 units of time to increase an initial value of 1200 to 2400 at a rate of 0.105 exponentially!

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