Today we are going to discuss about exponential functions that are applied in real life situation. Here are some of real-life examples
Population Growth
Exponential Decay
Compound Interest
Population Growth's general formula will be y = yo(n)^t/T
In the formula, yo stands for y initial if you are wondering. Also, the n depends on if the statements specifies if it doubles or triples, vice versa. t represents the time and T represents the time when it doubles/triple/vice versa.
Here is an example on how we can evaluate this formula.
There are 20 bacteria present, and it doubles every 5 hours.
Here is the conducted formula based on the situation
y = 20(2)^t/5
Now what happens when 30 hours have passed?
y = 20(2)^30/5
y = 20(2)^6
y = 20(64)
y = 1280
There are 1280 bacteria present after 30 hours.
Exponential Decay's general formula will be y = yo(1/2)^t/T
In the formula, yo represents the initial, t represents the time and T represents the time when it divides.
Here is an example on how we can evaluate this formula.
There are 30g of mercury present, and it will decay after 10 hours.
Here is the conducted formula based on the situation:
y = 30(1/2)^t/10
Now, what happens to the amount after 30 hours have passed.
y = 30(1/2)30/10
y = 30(1/2)^3
y = 30(0.125)
y = 3.75
There will be 3.75g of mercury after 30 hours.
Compound Interest's general formula will be A = P(1 + r)^t
In this formula, P represents the money. The r represents the rate, usually represented in decimal form. Finally t represents the time.
Here is an example of this real-life situation.
Maria wants to borrow money in the bank. She went to the bank and borrowed 2,000 pesos. She is aware that if one month has passed, the interest will increase her debt. The interest rate is 10%. If she didn't pay back her debt for 5 months, how much money she will pay?
Here is the formula conducted based on the question.
A = 2000(1 + 0.10)^5
A = 2000(1.10)^5
A = 2000(1.61051)
A = 3221.02
She will have to pay 3221.02 pesos debt to the bank.
Thanks for reading!
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