We solve this by the definition of slope in analytical geometry. The definition of slope is the rise over run. In equation, that would be

m = Δy/Δx = (y₂-y₁)/(x₂-x₁)

The x-coordinates here are the t values, while the y-coordinates are the f(t) values. So, let's find the y values of the boundaries.

At t=2: f(t)= 0.25(2)²<span> − 0.5(2) + 3.5 = 3.5
Point 1 is (2, 3.5)
At t=6: </span>f(t)= 0.25(6)² − 0.5(6) + 3.5 = 9.5
Point 2 is (6, 9.5)

The slope would then be

m = (9.5-3.5)/(6-2)
m = 1.5

Hence, the slope is 1.5. Interpreting the data, the rate of change between t=2 and t=6 is 1.5 thousands per year.

5 0

3 years ago

Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. What is the

vodomira [7]

Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. The rate of change is 391.5 % increase

<em><u>Solution:</u></em>

Given that Two years ago, Sally had 5,000 dogs in her dog shelter

Now she has 24,575 dogs

To find: rate of change

A rate of change is a rate that describes how one quantity changes in relation to another quantity

<h3><u>Steps to follow:</u></h3>

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number.

Then: divide the increase by the original number and multiply the answer by 100.

% change = Increase ÷ Original Number x 100

$\text {rate of change }=\frac{\text { new value }-\text {original value}}{\text {original value}} \times 100$

$\begin{array}{l}{\text { rate of change }=\frac{24,575-5000}{5000} \times 100} \\\\ {\text { rate of change }=\frac{19575}{5000} \times 100=391.5}\end{array}$

Thus the rate of change is 391.5 % increase

5 0

3 years ago