Question

A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time period?
The rate of change in profit for this time period is $1$$ per month.

Answer 1

Rate of change of profit for this period is $2750 per month

Solution:

Given that,

Profit of $6500 in January and $17,500 in May

To find: Rate of change

Since,

January is the first month of the year (1) while May is the fifth month (5)

Therefore, we get two points

(1, 6500) and (5, 17500)

Using these points we can find the rate of change in profit for this time period

The rate of change using the following formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

Here from the points,

$(x_1, y_1) = (1, 6500)\\\\(x_2, y_2) = (5, 17500)$

Therefore, rate of change is given as:

$m = \frac{17500-6500}{5-1}\\\\m = \frac{11000}{4}\\\\m = 2750$

Thus rate of change of profit for this period = $2750 per month