Graphing Exponential Growth

When an amount grows at a fixed percent per unit time, the growth is exponential. To find $A_0$ we use the fact that $A_0$ is the amount at time zero, so $A_0=10.$ To find $k,$ use the fact that after one hour $\left(t=1\right)$ the population doubles from $10$ to $20.$ The formula is derived as follows

so $k=\ln (2).$ Thus the equation we want to graph is $y=10e^{(\ln 2)t}=10{(e^{\ln 2})}^t=10·2^t.$ The graph is shown in Figure 5.

Figure 5 The graph of $y=10e^{\left(\ln 2\right)t}$