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Write an exponential function to model each situation. Find each amount after the
Write an exponential function to model each situation. Find each amount after the
specified time.
A population of 1,236,000 grows 1.3% per year for 10 years
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The formula would be y = 1,236,000(1.3)^t
After 10 years, the population would grow to become 17,039,309.59 people. You can round up to 17,039,310 people if the question asks to round to the nearest person.
There are many ways in which we can find for the zeros of the problem. We can use the quadratic formula, completing the square, using a graphing calculator, etc.
For this problem, I'll be completing the square.
x² - 6x = -22
Since the constant has been moved to the right side already, we can move on to the next step which is adding (b/2)² to both sides of the equation.
x² - 6x + (-6/2)² = -22 + (-6/2)²
x² - 6x + 9 = -22 + 9
Factor the left side of the equation into a perfect square and simplify the right side.
(x - 3)(x - 3) = -13
Take the square of both sides.
x - 3 = ± √-13
Take out the negative from the square root as the letter "i"
x - 3 = ± i√13
Add 3 to both sides of the equation to let x be by itself.
x = 3 ± i√13
So your two roots will be:
x = 3 + i√13 and x = 3 - i√13
Solution: C. 3 - i√13