Question

The population of a region is growing exponentially. There were 40 million people in 1990 (t = 0) and 70 million in 2000. Find an expression for the population at any time t, in years. Use the general exponential function and remember to use exact values.


P(t) = (in millions)

What population would you predict for the year 2010?
______ million people

What is the doubling time? (Round your answer to one decimal place.)
_________years

Answer 1

you can use
\[40\times \left(\frac{7}{4}\right)^{\frac{t}{10}}\]if you like although i doubt that is what the teacher had in mind, it is the easiest

Answer 2

since 2010 is 20 years after 1990 the answer to the second question would be
\[40\times \left(\frac{7}{4}\right)^{\frac{20}{10}}=40\times \left(\frac{7}{4}\right)^{2}\]
\[=122.5\]

Answer 3

whats the doubling time?