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?
3 answers
b,d,e,a,f,c**
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.
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.
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
a. 200, 2000
b. 18, 54
c. 50, 250
d. 50, 500
e. 4.5 , 13.5
f. 12.5 , 62.5