Question

For x > 1 order the following functions from steepest to shallowest.
a. y=2(10)^x
b. y=2(3)^x
c. y=2(5)^x
d. y=1/2(10)^x
e. y=1/2(3)^x
f. y=1/2(5)^x

I think the order would be b,d,e,a,f,g but I am not very good at this, could someone help me with what the order would be?

Answer 1

b,d,e,a,f,c**

Answer 2

the larger the base, the steeper the growth. Now, around x=0, the steepness also depends on the leading coefficient, but once you get to larger x values, any kind of 10^x will be steeper than any possible 3^x

So the order will be 10^x > 5^x > 3^x
after that, order by decreasing order of leading coefficients. That makes the correct order
a, d, c, f, b, e

Using some calculus, you can find just where faster functions overtake the slower ones, but that appears to be beyond the scope of this question.

Answer 3

try them for x = 2 and x = 3
a. 200, 2000
b. 18, 54
c. 50, 250
d. 50, 500
e. 4.5 , 13.5
f. 12.5 , 62.5