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Answer:
In 20 years, the population will be about 80.3 thousand people
Step-by-step explanation:
If our first time is 0 and the population that goes along with that time is 70,000, we have a coordinate point where x is the time (0), and y is the population at that time (70). Our next time is 10 years later, when the population is 75,000. The coordinate point for that set of data is (10, 75). Now we will use those 2 points in the standard form of an exponential equation to write the model for this particular situation.
Exponential equations are of the form
where x and y are the coordinates from our points, one at a time; a is the initial value, and b is the growth rate. Filling in an equation with the first set of data:
Anything raised to the power of 0 = 1, so b to the power of 0 = 1 and we simply have that a = 70.
Now we use that value of a along with the x and y from the next coordinate pair to solve for b:
Begin by dividing both sides by 70 to get
Undo the power of 10 on the right by taking the 10th root of both sides:
On the right side we simply have b now, and on the left we have
1.006923142=b
Now we have a and b to write the model for this situation:
We need to find y, the population, in x = 20 years:
Raise the parenthesis to the 20th power giving you
y = 70(1.147959784) and
y = 80.3 thousand people