Question

The population of a certain state from 2000 to 2010 was recorded. During that​ decade, the state grew from 19.3 million in 2000 to 24.1 million in 2010. Use an exponential growth model to predict the population of the state in 2035 . Let​ y(t) be the population of the​ state, in​ millions, t years after the year 2000. Give the exponential growth function for this​ state's population. y (t ) = ___________.

Answer 1

Answer:

Population in 2035 is 41.9 millions.

Step-by-step explanation:

We are given the following information in the question:

The population grew from 19.3 million in 2000 to 24.1 million in 2010.

We have to use exponential growth model to predict the population of the state in 2035.

Exponential growth function for this​ state's population is given by:

$y(t) = Ae^{kt}$

where A is constant and t is number of years after 2000.

In year 2000, the population is 19.3 million

$y(0) = 19.3 = Ae^0\\A = 19.3$

In year 2010, the population is 24.1

$y(10) = 24.1 = 19.3e^{10k}\\\\k = \displaystyle\frac{1}{10} \log \frac{24.1}{19.3} = 0.0222106$

Population of the state in 2035 =

$y(35) = 19.3e^{(0.0222106)(35)} \approx 41.9918728$

Thus, population in 2035 is 41.9 millions.

Answer 2

Answer:

a

Step-by-step explanation: