The population of a region is growing exponentially. There were $25$ million people in $1980($when $t=0)$ and $80$ million people in $1990$ Find an exponential model for the population $($in millions of people$)$ at any time $t,$ in years after $1980.$

$($Note: if you use decimal approximations for the numerical constants in your work, be sure to retain enough significant figures through your work to ensure that subsequent answers are correct$)$

$P(t)=$

What population do you predict for the year $2000?$

Predicted population in the year $2000=$

What is the doubling time?

Doubling time $=$ million people

years