Exponential Growth with a = 1000000000000, r = 0.02, p = 7400000000
Enter 3 out of 4 items below
You start with an initial value of 7400000000
This accumulates to exponentially to 1000000000000 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:
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 = 2.718281828459
Plugging in our known values, we get:
7400000000e0.02t = 1000000000000
Step 1: Divide each side of the equation by 7400000000 to isolate (t):
| 7400000000e0.02t | |
| 7400000000 |
| 1000000000000 |
| 7400000000 |
Step 2: Cancel the 7400000000 on the left side:
e0.02t = 135.13513513514
Step 3: Take the natural log Ln of both sides of the equation to remove e:
Ln(e0.02t) = Ln(135.13513513514)
There exists a logarithmic identity which states: Ln(en) = n, so we have
0.02t = 4.906275278772
Step 4: Divide each side of the equation by 0.02 to isolate (t):
| 4.906275278772 |
| 0.02 |
Step 5: Cancelling 0.02 on the left side of the equation and simplifying the right, we can solve for (t):
t = 245.3137639386
Summary:
Final Answer:
Therefore, it would take 245.3137639386 units of time to increase an initial value of 7400000000 to 1000000000000 at a rate of 0.02 exponentially!
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What is the Answer?
Therefore, it would take 245.3137639386 units of time to increase an initial value of 7400000000 to 1000000000000 at a rate of 0.02 exponentially!
How does the Exponential Growth Calculator work?
Free Exponential Growth Calculator - This solves for any 1 of the 4 items in the exponential growth equation or exponential decay equation, Initial Value (P), Ending Value (A), Rate (r), and Time (t).
This calculator has 4 inputs.
What 2 formulas are used for the Exponential Growth Calculator?
Pert = Ae is Eulers Constant = 2.718281828459
For more math formulas, check out our Formula Dossier
What 5 concepts are covered in the Exponential Growth Calculator?
decayReduction in size from decompositionexponentialof or relating to an exponentexponential growthgrowth whose rate increase in proportion to the total numberratethe ratio between two related quantities in different units. A measure, quantity, or frequency.timea point of time as measured in hours and minutes past midnight or noonExample calculations for the Exponential Growth Calculator
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