Choose two consecutive points on the graph and find the rate of change.
We will start with t = 1000 and t = 1500:
[tex]P(1000)=12.643(1.0027)^{1000}=187.4412[/tex][tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex]
Remember that the rate of change is found by the difference in y over the difference in x.
[tex]RATEOFCHANGE=\frac{721.7263-187.4412}{1500-1000}[/tex][tex]RATEOFCHANGE=\frac{534.2851}{500}\approx1.0686[/tex]
Let's do it now for t = 1500 and t = 2000.
[tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex][tex]P(2000)=12.643(1.0027)^{2000}=2778.9454[/tex]
In this case the rate of change would be:
[tex]\text{rateofchange=}\frac{2778.9454-721.7263}{2000-1500}[/tex][tex]\text{rateofchange}=\frac{2057.2191}{500}\approx4.1144[/tex]
The slopes are different and due to the type of function they will always increase when taking larger values.
