A population of 350 animals has a growth rate of 5% each year. Write an exponential function to model this situation.

Given:

The population of animals = 350

Growth rate = 5% each year.

To find:

The exponential function to model this situation.

Solution:

The general exponential growth model is:

Where, a is the initial value, r is the growth rate in decimal and t is the time period.

Substituting in the above formula, we get

Therefore, the required exponential function is , where f(t) is the number of animals after t years.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: