In what year 200, the population of Virginia was about 7,400,000.

Between the years 200 and 2004, the population in Virginia grew at a rate of 5.4%. At this growth rate, the function f (x) = 7,400,000 (1.054) ^x

gives the population x years after 2000.

9.) In what year will the population reach 15,000,000?

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For this case we have the following function:

f (x) = 7,400,000 (1,054) ^ x

Where,

x represents time in years.

Substituting f (x) = 15000000 we have:

15000000 = 7,400,000 (1,054) ^ x

Clearing x we have:

(1,054) ^ x = (15000000) / (7400000)

log1.054 ((1.054) ^ x) = log1.054 ((15000000) / (7400000))

x = log1.054 ((15000000) / (7400000))

x = 13.4 years

Rounding to the nearest year:

x = 14 years

Answer:

the population will reach 15,000,000 in 2014.