# Exponential Growth with a = 2, r = 1.26480934686, p = 1, t =

Enter 3 out of 4 items below. Leave the item you want to calculate blank:
Final ValueInitial ValueRateTime

You start with an initial value of 1 which accumulates to 2 at a rate of 1.26480934686 exponentially. How long did this take?:

Since r = 1.26480934686 is greater than zero, we have an exponential growth equation

The exponential growth equation is as follows:
Pert = 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.

Plugging in our known values, we get:
1e1.26480934686t = 2

Step 1: Divide each side of the equation by 1 to isolate (t):
 1e1.26480934686t 1
 =
 2 1

Step 2: Cancel the 1 on the left side:
e1.26480934686t = 2

Step 3: Take the natural log Ln of both sides of the equation to remove e:
Ln(e1.26480934686t) = Ln(2)
There exists a logarithmic identity which states: Ln(en) = n, so we have
1.26480934686t = 0.95

Step 4: Divide each side of the equation by 1.26480934686 to isolate (t):
 1.26480934686t 1.26480934686
 =
 0.95 1.26481

Step 5: Cancelling 1.26480934686 on the left side of the equation and simplifying the right, we can solve for (t):
t = 0.34

Summary:
Therefore, it would take 0.34 units of time to increase an initial value of 1 to 2 at a rate of 1.26480934686 exponentially!