Question

Where could exponential functions be used in the real world? Explain.

Answer 1

Any investment that compounds interest rate is one example of an exponential function.
Radioactive isotopes decay at an exponential rate.
Bacteria grows in a culture at an exponential rate.

Answer 2

The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts.

Answer 3

For example, the compound interest formula: \[\Large A = P(1 + \frac{ r }{ n })^{nt}\]A = Amount at maturity
P = Principal Amount invested
r = Annual interest rate
n = compounding period (compounded how many times a year)
t = years invested

The exponent (n * t) makes this an exponential function.

Answer 4

Also there are many instances where exponential functions in real life can occur, essentially path integrals/functional integrals are used for quantum mechanics.

Answer 5

These answers are more helpful and more interesting than I thought they would be. Thank you!

Answer 6

Your welcome

Answer 7

yw. :)

Answer 8

Radioactive substances such as uranium steadily decay meaning they lose their mass which gets converted to energy/radiation. There is a term that is used called "half-life". If half-life of a substance is 5 years, it means that substance will be half its original mass in 5 years.

If you start with one bacteria and it doubles every second, for example.
Then the bacteria will grow as follows: 1, 2, 4, 8, 16, etc.
The number of bacteria at time t will be an exponential function: 2^x.

Answer 9

That is a very resourceful response of exponential functions.