A city population, which was initially 15,500, has been dropping by 3% a year. Write an exponential function and graph the function. Use your graph to predict when the population will drop below 8,000.

How do I solve this?

Question

A city population, which was initially 15,500, has been dropping by 3% a year. Write an exponential function and graph the function. Use your graph to predict when the population will drop below 8,000. 

How do I solve this?

anonymous · Answer

to decrease a number by 3% multiply it by $100\%-3\%=97\%=.97$
to do it $x$ times, multiply by $.97^x$
your job is to solve 
$$15,500(.97)^x=800$$

anonymous · Answer

Thank you SO much!

anonymous · Answer

here is a picture of the graph on the interval $[0,30]$ http://www.wolframalpha.com/input/?i=15500%28.97%29^x+domain+1..30

anonymous · Answer

you can solve for 
$$15500(.97)^x=8000$$ by using logs or else solve from the graph

anonymous · Answer

looks like just under 22 years http://www.wolframalpha.com/input/?i=15500%28.97%29^x%3D8000 yw

anonymous · Answer

Thank you ! :)))