Exponential Growth Graph

The exponential growth graph is nothing but the exponential function occurs if the rate of growth is proportional to the functional value and the current value in the functional part. The exponential graph contains some of the equal intervals and can be called as the exponential growth or exponential decay. Now we are going to see about the exponential growth graph.
Problems on Exponential Growth Graph

Determine the exponential growth for the function $3000 and to double at 21/2 % continuously

Solution:

The exponential growth function can be calculated as,

A = Pert

The rate value which can be taken as 0.105

6000 = 3000 e 0.105t

We have to take natural log on both sides we get,

2 = e0.105t

ln 2 = ln e 0.105t

ln 2 = 0.105t (ln e)

ln 2 = 0.105t

By using the calculator the value can be found as,

0.693147 = 0.105t

t = 6.666

Thus it takes 6.66 years to double the money.

Graph:Graph
More Problems on Exponential Growth Graph:

Example 1:

Determine the value of ‘r’ where A = 50 at t = 6 years and P = 10

Solution:

The exponential growth can be calculated as,

A = Pert

50 = 10 e6r

5 = e6r

The logarithm for the above equation given as,

ln 5 = 6r

ln (5)/6 = r

r = 1.6094/6

r = 0.2682

The growth of exponential is 0.2682.

Example 2:

Determine the exponential growth for the function $4000 and to double at 24/2 % continuously

Solution:

The exponential growth function can be calculated as,

A = Pert

The rate value which can be taken as 0.12

8000 = 4000 e 0.12t

We have to take natural log on both sides we get,

2 = e0.12t

ln 2 = ln e 0.12t

ln 2 = 0.12t (ln e)

ln 2 = 0.12t

By using the calculator the value can be found as,

0.693147 = 0.12t

t = 5.77

Thus it takes 5.77 years to double the money.

Graph:

Graph