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baherus [9]
2 years ago
7

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage r

ate of increase or decrease.
y=570(0.98)^x
Mathematics
1 answer:
IceJOKER [234]2 years ago
4 0

Answer:

decay

2% decrease

Step-by-step explanation:

The growth factor is the base of the exponent: 0.98. Its relation to the rate of change is ...

 growth factor = 1 + rate of change

 0.98 = 1 + (-0.02)

So, the rate of change is -0.02 = -2%. Since the rate of change is a 2% decrease, it represents decay.

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What is the equation of the line?
spin [16.1K]

Answer:

y=1/2x+2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(0,2) and (-4,0).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (-4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m= 0 - 2-4 - 0 or... m= -2-4 or... m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(-4,0). When x of the line is -4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (-4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=1/2 × 0+b, or solving for b: b=2-(1/2)(0). b=2.

(-4,0). y=mx+b or 0=1/2 × -4+b, or solving for b: b=0-(1/2)(-4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (-4,0)

is

y=1/2x+2

4 0
3 years ago
A train travels 68 kilometers in 2 hours, and then 64 kilometers in 3 hours. What is its average speed
skad [1K]
Average speed is the distance traveled by an object in total and divided by the amount of time an object covers the distance. The formula is -
Average speed = total distance traveled / total time taken
                         = 68km+64km / 2 hrs.+3hrs.
                         = 132km / 5hrs.
                         = 26.4km/hr.
Therefore, the train's average speed is 26.4km/hr.
5 0
3 years ago
Charles needed 3/4 cups of rasins. if he has a 1/4 measuring cup, how many times will he need to fi'll it up to get to the right
koban [17]
3 times because if he needs 3/4 cup the. you should use it 3 times. (3/4÷1/4=3)
7 0
3 years ago
What is the value of x three times less than the value of 45−10x?
Mekhanik [1.2K]
This is the concept of algebra. The value of x three times less than the value of 45-10x will be as follows;
The value of x three times is:
3x
subtracting 45-10x we get:
3x-(45-10x)
3x+10x-45
13x-45
the answer is:
13x-45
6 0
3 years ago
Find the slope of (9,8) and (5,1)
8_murik_8 [283]

Answer:

Slopem=74

As a decimal:

m = 1.75

Step-by-step explanation:

8 0
2 years ago
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