If the population of a country is growing at a rate of 2.2% compounded
1 answer:
It will take 31.9 years.
The general form of this equation is
y = a(1+r)ˣ, where y is the total population, a is the initial population, r is the growth rate as a decimal number, and x is the amount of time. For our problem, we have
120000 = 60000(1+0.022)ˣ
[The 120,000 is because we are doubling the 60,000 population]
Dividing both sides by 60,000,
120000/60000 = 60000(1+0.022)ˣ/60000
2 = 1.022ˣ
Using logarithms to solve this, we have
The general form of this equation is
y = a(1+r)ˣ, where y is the total population, a is the initial population, r is the growth rate as a decimal number, and x is the amount of time. For our problem, we have
120000 = 60000(1+0.022)ˣ
[The 120,000 is because we are doubling the 60,000 population]
Dividing both sides by 60,000,
120000/60000 = 60000(1+0.022)ˣ/60000
2 = 1.022ˣ
Using logarithms to solve this, we have
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Answer:
(a) (5, -3)
Step-by-step explanation:
The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.
<h3>Expression to substitute</h3>The given equations are ...
- y = x -8
- 2x +3y = 1
We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.
<h3>Substitution</h3>When the expression (x-8) is substituted for y in the second equation, you get ...
2x +3(x -8) = 1
This simplifies to ...
5x -24 = 1
<h3>Solution</h3>This 2-step equation can now be solved in the usual way:
5x = 25 . . . . . . add 24 to isolate the variable term
x = 25/5 = 5 . . . . . divide by the coefficient of x
Note that we now know what the correct answer choice is.
Using the expression for y, we find ...
y = x -8 = 5 -8 = -3
The solution is (x, y) = (5, -3).
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The attached graph confirms this solution.
