Write an exponential equation in the form y = a(b)^x that can model the town population, y, x decades after this census was taken.
Understand the Problem
The question asks us to create an exponential equation reflecting the population growth of Valley View over time, given its current population and the percentage increase per decade.
Answer
$y = 1800(1.12)^x$
Answer for screen readers
The exponential equation is: $$ y = 1800(1.12)^x $$
Steps to Solve
- Identify the variables In the equation (y = a(b)^x):
- (y) is the future population.
- (a) is the current population (1,800).
- (x) is the number of decades after the census.
- (b) is the growth factor.
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Determine the growth factor The population is expected to grow by 12% each decade. The growth factor can be calculated as: $$ b = 1 + \text{(growth rate)} = 1 + 0.12 = 1.12 $$
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Write the exponential equation Substituting the values of (a) and (b) into (y = a(b)^x): $$ y = 1800(1.12)^x $$
The exponential equation is: $$ y = 1800(1.12)^x $$
More Information
This equation models the population of Valley View, where (y) represents the population (x) decades after the current census, with a consistent growth rate of 12% per decade.
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