Our function is something like
[tex]y=ae^{bx}[/tex]
When the city was founded, 0 years have passed. So, we want
[tex]y(0)=1000 \iff ae^{0x}=1000 \iff a\cdot 1 = 1000 \iff a=1000[/tex]
So, we can update our function: now we know that it will be something like
[tex]y=1000e^{bx}[/tex]
Similarly, we have to impose [tex]y(1)=1050[/tex]. Since
[tex]y(1)=1000e^{b\cdot 1}=1000e^b[/tex]
we have to impose
[tex]1000e^b=1050 \iff e^b = 1.05 \iff b = \ln(1.05)[/tex]
So, our function is
[tex]y=1000e^{\ln(1.05)x}[/tex]
