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Explanation:
Check out the image below. I've posted the synthetic division table. The value at the very end of the bottom row is the remainder. By the remainder theorem, this is exactly the value of g(-5).
Recall the remainder theorem says: If you divide p(x) by (x-k), then the remainder is p(k). In this case, k = -5 is our test root which is the value placed in the box on the left.
As a way to check the answer, we can say
g(x) = 2x^2 + 6x + 5
g(-5) = 2(-5)^2 + 6(-5) + 5
g(-5) = 25
So the answer is confirmed.
Answer: .
Step-by-step explanation:
It is given that,
Initial population of a town = 2000
Growth rate = 4% = 0.04 per year
The exponential growth function for population is
where, is initial population, r is growth rate and t is number of years.
Substitute in the above equation.
Therefore, the required equation is , where P is population after t years.