Exponential Growth Formula

A function is said to be Exponential growth that including exponential decay when the growth rate of that mathematical function is proportional to the function's current value. In a discrete domain of definition with equal intervals of the function is called as geometric growth or geometric decay. The exponential growth model is also called as the Malthusian growth model.


Exponential growth formula:

Exponential formula defines the  X as exponentially on time t.

X(t) = a . b(t/r)

"a" denotes the initial value

a = x,

X(0) = a,

b= a

It denotes the positive growth of the factor, t = time required

Example for exponential growth formula:

If a power doubles every 5 minutes, initially there’s only one doubles, how many powers would be there after 2 hours?

Here, a= 1, b= 2, t = 5 minutes.

X(t) = a . b(t/r) = 1 . 2{(120 minutes)/(5 minutes)}

X(2 hour) = 1 . 2 24 = 16777216

After two hours, there would be 16777216 powers.


Exponential growth Problem:

A microbiologist is researching a newly-discovered species of fungi. At time t = 0 hours, he puts one hundred fungi into what he has determined to be a favorable growth medium. Six hours later, he measures 200 fungi. Assuming exponential growth, what is the growth constant "i" for the fungi? (Round i to two decimal places.)

For the given problem, the units on time t will be hours, because the growth is being measured in terms of hours. The starting amount P is the amount at time t = 0, so, for this problem, P = 100. The ending amount is A = 200 at t = 6. The only variable we don't have a value for is the growth constant i, which also happens to be what I'm looking for. So I'll plug in all the values we know, and then solve for the growth constant:
A = Peit
200 = 100e6i
2 = e6i
ln(2) = 6i
`ln(2)/6` = i = 0.11552453