Answer:
- y = 78918·1.06^x
- about 4.063 years
Step-by-step explanation:
You want the time it take for a population of 78,918 to grow to 100,000 at the rate of 6% per year.
Equation
The population can be described by ...
y = ab^x
where 'a' is the initial population, and 'b' is the growth factor. The growth factor is ...
b = 1 + growth rate = 1 + 6% = 1.06
The initial population is given as 78,918, so the equation for the population in x years is ...
y = 78918·1.06^x . . . . . population in x years
Time
Solving for x when y = 100,000 gives ...
100000 = 78918·1.06^x . . . . . . use desired y value
100000/78918 = 1.06^x
log(100000/78918) = x·log(1.06)
x = log(100000/78918)/log(1.06) = -log(0.78918)/log(1.06) ≈ 4.063
The best prediction of the time it will take for the population to reach 100,000 is 4.063 years.
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Additional comment
That's about 4 years and 23 days.
