Question

The populations P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by

Answer 1

Answer:

Explained below.

Step-by-step explanation:

The population model for Orlando, Florida from 2000 through 2007 is:

$P = 1656.2\times e^{kt}$

It is provided that, in 2005, the population of Orlando was about 1,940,000.

(a)

Compute the value of k as follows:

For year 2005, the value of t is 5.

$P = 1656.2\times e^{kt}$

$1940000=1656.2\times e^{k\times 5}\\\\e^{k\times 5}=\frac{1940000}{1656.2}\\\\e^{k\times 5}=1171.35612\\\\5k=\ln(1171.35612)\\\\k=\frac{7.06592}{5}\\\\k=1.413184\\\\k\approx 1.41$

Since the value of k is positive, the population is increasing.

(b)

Compute the populations of Orlando in 2010 as follows:

$P = 1656.2\times e^{kt}$

   $=1656.2\times e^{1.41\times 10}\\\\=2201227729.68\\\\\approx 2,201,227,730$

Compute the populations of Orlando in 2015 as follows:

$P = 1656.2\times e^{kt}$

   $=1656.2\times e^{1.41\times 15}\\\\=2537704633019.96\\\\\approx 2,537,704,633,020$

Since the population increased exponentially from 2010 to 2015, yes the results are reasonable.