This is algebra 2 it’s growth & decay. I need help
1 answer:
<h3>Part 1:</h3>
So firstly, remember that the <em>a variable is the initial value.</em> Since we start off with 6.08 billion, <u>6.08 billion is the a variable.</u>
Next, since this is a <em>growth by 1.26%</em>, add 1 and 0.0126 (1.26% in decimal form) together to get 1.0126. <u>1.0126 is the b variable.</u>
Putting it together, <u>the function is </u>
Since 2020 is 20 years from 2000, plug in 20 into the t variable of the prior function to solve:
In context, <u>in 2020 the population will be 7.81 billion.</u>
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Answer:
(x, y, z) = (1, -3, 1)
Step-by-step explanation:
Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:
(x, y, z) = (1, -3, 1)
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Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.
Using the first equation to write an expression for z, we have ...
z = 4x +3y +6
Substituting that into the second and third equations gives ...
6x -y +3(4x +3y +6) = 12 ⇒ 18x +8y = -6
8x +2y +4(4x +3y +6) = 6 ⇒ 24x +14y = -18
Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:
3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)
10y = -30
y = -3
Substituting into the first equation (of the equations in x and y), we have ...
18x +8(-3) = -6
18x = 18
x = 1
Finally, substituting into the equation for z gives ...
z = 4(1) +3(-3) +6 = 1
The solution is (x, y, z) = (1, -3, 1).
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The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.
