In the year 2000, the population of virginia was about 7,400,000. after 2000, the population of virginia grew at a rate of 5.4%. the function f(x)=7,400,000(1.054)^x gives the population x years after 2000.

Question

is the population growing or decaying?
at what rate is the population increasing or decreasing?
what does the 7,400,000 represent?.

what was the size of the population after 5 years?.

Answer 1

1. Is the population growing or decaying? The population is growing. Since the growth rate is positive (5.4%), it indicates that the population is increasing over time.

2. At what rate is the population increasing or decreasing? The population is increasing at a rate of 5.4% per year.

3. What does the 7,400,000 represent? The value of 7,400,000 represents the initial population of Virginia in the year 2000.

4. What was the size of the population after 5 years? To find the population after 5 years, substitute \( x = 5 \) into the function \( f(x) = 7,400,000(1.054)^x \):

   \[ f(5) = 7,400,000(1.054)^5 \]

   First, calculate \( (1.054)^5 \):

   \[ (1.054)^5 \approx 1.295618 \]

   Next, multiply this by 7,400,000:

   \[ f(5) \approx 7,400,000 \cdot 1.295618 \approx 9,573,571.2 \]

   Therefore, the approximate size of the population after 5 years (in the year 2005) would be about 9,573,571.