The population of a region for 2000 is 19.5 (in millions) . The predicted population (in millions) for the region in the year 2020 is 24. Find the constants C (to one decimal place) and k (to four decimal places) to obtain the experimental growth model $y=C{e}^{kt}$ for the population. (Let $t=0$ correspond to the year 2000.)

A) $y=19.5e^{0.0045t}$
B) $y=7.2e^{1.2076t}$
C) $y=19.5e^{0.2076t}$
D) $y=19.5e^{0.0104t}$
E) $y=7.2e^{0.0604t}$

We can use the given data to solve for C and k.

When t = 0 (corresponding to the year 2000), y = 19.5.
This gives us:

19.5 = C e ^ { k 0 }
19.5 = C

So we know that C = 19.5.

Now we can use the second piece of information to solve for k.

When t = 20 (corresponding to the year 2020), y = 24.
This gives us:

24 = 19.5 e ^ { k 20 }

Dividing both sides by 19.5:

1.230769231 = e ^ { k 20 }

Taking the natural logarithm of both sides:

ln(1.230769231) = ln(e ^ { k 20 })

ln(1.230769231) = k 20

k = ln(1.230769231)/20

k ≈ 0.0104 (rounded to four decimal places)

Therefore, the experimental growth model is:

y = 19.5 e ^ { 0.0104 t }