What is the y-coordinate of the solution of the system of equations? {y=3x−26 2x−y=19 Enter your answer in the box.
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Answer:
Step-by-step explanation:
This is your exponential growth function for population:
and these are your initial conditions with the year 2000 being t = 0
(0, 6.31) and (69, 12)
We will use those values to find the equation that models this population growth. In the coordinates, the first number is the time in years, t; the second number is the population after a certain time t goes by. In other words, the second number represents the A in our model. Using those values from the first set of coordinates will help us solve for A₀:
which is basically e raised to the power of 0 which is equal to 1, so we get from that first set of coordinates that A₀ = 6.31
Now we will use that along with the numbers in the second coordinate pair to find the value for k:
Begin by dividing both sides by 6.31 to get
and take the natural log of both sides since natural logs and e's undo each other:
Simplifying both sides give us:
.6427709734 = 69k so
k = .0093155
Now we can finally write the equation that models this population as
and we can answer the question about which year, x, will the population be 7 million, A.
Begin by dividing both sides by 6.31 to get
and again take the natural log of both sides:
and simplify to
.1037744728=.0093155t so
t ≈ 11
That means that in the year 2011 the population will be 7 million