Answer: y = 14^x
Step-by-step explanation:
Here the options are:
a y = 14^x
b y = -3*(17)^x
c y = 120x
d y = -275x
to see which function increases the fastest (or which function is steeper) we need to look at the first derivations of each one of these, and see which one is larger for every value of x:
the derivations are:
a y = x*14^(x - 1)
b y = -x*3*(17)^(x - 1)
c y = 120
d y = -275
So we can already discard options c and d, because have constant rate of change.
Then we keep options a and b.
Always when we have an exponential function, like a^x and b^x
The one with the larger base will be steeper.
So if a > b, then:
a^x is steeper than b^x
In this case, the function:
y = -3*(17)^x
has a larger base, but, this function is negative.
This means that as x increases, our function will decrease, then this function will not "increase the fastest" (because it does not increase)
Then the left option (a: y = 14^x)
Will be the correct one.
(this will happen after some value of x, because two of the options have constant derivatives, these may be steeper for smaller values of x, and as x increases, we will see that y = 14^x is the one that increases the fastest)
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