What does it mean wiun Something aows of daays exponen nally

What does it mean wiun Something aows of daays exponen nally? Researcn Share a rel ubntl problem situa tion, phenomuion,o vent hat can be modeledl Sinay exporential Cor post the mathematical model descnbing your Application if avai lable

Solution

Many real world situtaions can be modelled as exponentila growth or decay such as:

studies of populations, bacteria, the AIDS virus, radioactive substances, electricity, temperatures , bank credits etc

Exponential growth or decay means the quantity is varying exponentialy:

y(t) = a*e^kt

y(t) = value at time \"t\"
a = value at the start
k = rate of growth (when >0) or decay (when <0)
t = time

example : 3 years ago you had $ 100 in the bank. You now have $192.
If the amount of money at the end of each year increases exponentially, then how much will you have in the bank after another 7 years?

tart with the formula y(t) = ae^kt
We know y(0) = 100
100 = ae⁰
a = 100

We also know y(3) = 192
192 = 100e^3k
e^3k = 192 ÷ 100 = 1.92
3k = ln(1.92) = 0.652...
k = 0.652... ÷ 3 = 0.217...

Now we know a and k, we can write the growth function y(t) = ae^kt explicitly as
y(t) = 100e^0.217t

Now, we can find how much money there will be in the bank after a further 7 years by replacing t with 10:

y(10) = 100e^{0.217 × 10}
= 100e^2.17
= 100 × 8.758...
= 875.8

You will have $875.8 in the bank after a further 7 years