Exponential Growth with a = 1000000000000000000000000000000000, r = 0.02, p = 7400000000, t =

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You start with an initial value of 7400000000

This accumulates to exponentially to 1000000000000000000000000000000000 at a rate of 0.02

How long did this take?:

Since r = 0.02 > 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:

7400000000e^0.02t = 1000000000000000000000000000000000

Step 1: Divide each side of the equation by 7400000000 to isolate (t):

Step 2: Cancel the 7400000000 on the left side:

e^0.02t = 1.3513513513514E+23

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

Ln(e^0.02t) = Ln(1.3513513513514E+23)

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

0.02t = 53.260562231647

Step 4: Divide each side of the equation by 0.02 to isolate (t):

Step 5: Cancelling 0.02 on the left side of the equation and simplifying the right, we can solve for (t):

t = 2663.0281115823

Summary:

Final Answer:

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Tags:

• decay
• exponential growth
• exponential
• rate
• time