QuestionAntonio's county has a population of 66,500, decreasing by yearly. Model it with and find in 10 years.
Studdy Solution
STEP 1
Assumptions1. The current population is66,500 people. The population is decreasing by4% each year3. We are modeling the population with an exponential equation of the form
STEP 2
First, we need to identify the initial population, which will be the value of in our equation. This is the population at the start, or when .
STEP 3
Next, we need to identify the rate of change, which will be the value of in our equation. This is the percentage by which the population decreases each year, converted to a decimal and subtracted from1 (since the population is decreasing).
STEP 4
Now we can write the exponential equation that models the population of the county.
STEP 5
Substitute the values of and into the equation.
STEP 6
Now, to find the population in10 years, we substitute into the equation.
STEP 7
Calculate the expected population in10 years.
To the nearest hundred people, Antonio can expect the population of his county to be about49,100 people in10 years.
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