4-0.25g+0.5h= when g=10, h=5
2 answers:
You might be interested in
Answer:
- x-intercept: (-0.1, 0)
- Horizontal Asymptote: y = -3
- Exponential <u>growth</u>
(First answer option)
Step-by-step explanation:
<u>General form of an exponential function</u>
where:
- a is the initial value (y-intercept).
- b is the base (growth/decay factor) in decimal form:
If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function. - y=c is the horizontal asymptote.
- x is the independent variable.
- y is the dependent variable.
Given <u>exponential function</u>:
The x-intercept is the point at which the curve crosses the x-axis, so when y = 0. To find the x-intercept, substitute y = 0 into the given equation and solve for x:
Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.
<h3><u>Asymptote</u></h3>An <u>asymptote</u> is a line that the curve gets infinitely close to, but never touches.
The <u>parent function</u> of an <u>exponential function</u> is:
As<em> </em>x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.
Therefore, there is a horizontal asymptote at y = 0.
This means that a function in the form always has a horizontal asymptote at y = c.
Therefore, the horizontal asymptote of the given function is y = -3.
<h3><u>Exponential Growth and Decay</u></h3>A graph representing exponential growth will have a curve that shows an <u>increase</u> in y as x increases.
A graph representing exponential decay will have a curve that shows a <u>decrease</u> in y as x increases.
The part of an exponential function that shows the growth/decay factor is the base (b).
- If b > 1 then it is an increasing function.
- If 0 < b < 1 then it is a decreasing function.
The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.
Learn more about exponential functions here:
Answer:
the larger number is 50
Step-by-step explanation:
Notice there are two unknown numbers. Let's address the smaller one as x and the larger one as y. now we can write two equations from translating the phrases given into algebraic expressions:
"the sum of two numbers is 80" can be written as:
Now the second phrase:
"The ratio of those two numbers is 3/5"
Notice here that in our ratio we need to use our small number (x) in the numerator of the quotient, and the larger number (y) in the denominator to make it in agreement with the small and larger numbers of the ratio , and solve for x:
Replace the value of x we just obtained in the first equation we wrote, so we obtain one equation with only one unknown hat we should be able to solve:
Therefore the larger number (y) equals 50.