# There were 35 million people in 1980 (when t=0 ) and 80 million people in 1990. How do you find an exponential model for the population (in millions of people) at any time t, in years after 1980?

Nov 30, 2016

$y = 35 \cdot {\left(\frac{16}{7}\right)}^{\frac{t}{10}}$

#### Explanation:

The generic exponential model is:

$y = a {b}^{t}$

Use the data you have to determine $a , b$:

for $t = 0$:

$35 = a \cdot {b}^{0} = a$

for $t = 10$:

$80 = 35 {b}^{10}$

and then $b = {\left(\frac{80}{35}\right)}^{\frac{1}{10}}$

Finally:

$y = 35 \cdot {\left(\frac{16}{7}\right)}^{\frac{t}{10}}$