Question

Choose two consecutive points on the graph and find the rate of change. Is the slope the same or different?

Answer 1

Choose two consecutive points on the graph and find the rate of change.

We will start with t = 1000 and t = 1500:

`P(1000)=12.643(1.0027)^(1000)=187.4412`
`P(1500)=12.643(1.0027)^(1500)=721.7263`

Remember that the rate of change is found by the difference in y over the difference in x.

`RATEOFCHANGE=(721.7263-187.4412)/(1500-1000)`
`RATEOFCHANGE=(534.2851)/(500)\approx1.0686`

Let's do it now for t = 1500 and t = 2000.

`P(1500)=12.643(1.0027)^(1500)=721.7263`
`P(2000)=12.643(1.0027)^(2000)=2778.9454`

In this case the rate of change would be:

`\text{rateofchange=}(2778.9454-721.7263)/(2000-1500)`
`\text{rateofchange}=(2057.2191)/(500)\approx4.1144`

The slopes are different and due to the type of function they will always increase when taking larger values.