Question 129564: Which of the following is a growth curve?
a)y=0.6^x
b)y=(2/3)^-x
c)y=3.5^-x
d)y=2(1/3)^x
I think the answer is (d). Can someone please confirm???
Found 2 solutions by ilana, bucky:
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! This is tricky! Your answer is actually incorrect, but I was fooled at first as well. In order for a curve to be a growth curve, it must be of the form a(b)^x, where b is a number greater than 1. When the exponent is -x, that is the same as saying a(1/b)^x. For most of these, a=1. So the choices are:
a) y=(6/10)^x
b) y=(3/2)^x
c) y=(2/7)^x
d) y=2(1/3)^x
Can you see now which one has a b>1?
The answer is b, because 3/2, the growth factor, is greater than 1. The rest will get smaller as x gets bigger.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! The correct answer is answer b.
.
Let's look at a quick way to tell.
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First let's look at answer a). If x is zero, then y = (0.6)^0 and when you raise a number to
the zero power, the answer is 1. What happens if we next let x = 1? When x = 1 then the
equation for y is y = (0.6)^1 = 0.6. Right away we can see that as x increased from 0 to 1
that y decreased from 1 to 0.6 ... this is a decreasing graph and not a growth curve.
.
Next let's look at answer c). If x is 0 then y = (3.5)^-0 = (3.5)^0 = 1. Next let's let x = 1.
Then y becomes y = (3.5)^(-1) = 1/(3.5) = 0.2857. Therefore, as x increased from 0 to 1, the
value of y decreased from 1 to 0.2857
.
Then let's look at answer d). If x is 0 then y = 2*(1/3)^0 = 2*1 = 2. Now let x = 1 and
the value of y becomes y = 2*(1/3)^1 = 2*(1/3) = 2/3. So when x increased from 0 to 1, the
corresponding value of y decreased from 2 to 2/3. This is not a growth curve.
.
Finally let's look at answer b). When x equals 0 then y = (2/3)^(-0) = (2/3)^0 = 1. Now let x
grow to 1 and the corresponding value of y becomes (2/3)^(-1) = 1/(2/3)^1 = 1/(2/3) = 3/2
So when x goes from 0 to 1, y increased from 1 to 3/2. This increasing y with increasing x
represents a growth curve. Therefore, b) is the correct answer.
.
Hope this quick method helps you to see how you can determine if a curve is a growth curve.
You can try other values of x in each answer ... for example, let x = 2 and you should get
the same result ... only in answer b) will the value of y increase as x goes from 1 to 2.
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