Question

Describe a setting where you could use exponential functions to make investment decisions.

What kind of information could exponential functions tell you that would be valuable?

Answer 1

A) Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. On a chart, this curve starts slowly, remaining nearly flat for a time before increasing swiftly as to appear almost vertical. It follows the formula:

V = S * (1 + R) ^ T

The current value, V, of an initial starting point subject to exponential growth, can be determined by multiplying the starting value, S, by the sum of one plus the rate of interest, R, raised to the power of T, or the number of periods that have elapsed.

Compound interest is the best illustration of the investiment and profit.
Here great amount of profit is obtained with the course of time by a investment of lesser money.

A = P(1+r/n)^nt

where,

A - the amount of money after a certain amount of time
P - the principle or the amount of money you start with
r - the interest rate and is always represented as a decimal
n - the number of times interest is compounded in one year

   if interest is compounded annually then n = 1
if interest is compounded quarterly then n = 4
if interest is compounded monthly then n = 12
t - the amount of time in years.

B) Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications.

i)Population

Many times scientists will start with a certain number of bacteria or animals and watch how the population grows.It gives information/predict about population for a certain time .

P = P₀e^kt​​​​

ii) Radioactive Decay

Exponential function is very important in determining the disintegration of any radioactive element.

It predicts how much of substance will be left after some particular time.

Here we take negative exponent (decrease)

M=M_oe^-kt​​​​