Question

Is the function below exponential?
G(t)= (4 . t)^4

If so, write the function in the form G(t)=ab^t and find the value for a and b.
How do I do this question?

Answer 1

Is this what the function looks like?\[\Large\rm G(t)=(4t)^4\]

Answer 2

G(t) = (4*t)^4

Answer 3

Multiplication..?
Yah so that's implied in what I wrote..

Answer 4

well it shows up as a dot. So I imagine it is a multiplication

Answer 5

So we need to see whether or not we can get it into this form:\[\Large\rm G(t)=\color{orangered}{a}\color{royalblue}{b}^t\]

Answer 6

Remember your exponent rule?\[\Large\rm (ab)^c=a^c~b^c\]

Answer 7

Applying this rule gives us:\[\Large\rm G(t)=4^4~t^4\]

Answer 8

Hmm looks like this is a `polynomial function`, not an exponential one.
See how our variable is the `base`?

Unless we're misinterpreting the dot lol

Answer 9

Okay so to be exponential we would need the variable in the c position (not the base)

Answer 10

ya c:

Answer 11

And since it is not, then it is a polynomial function.

Answer 12

Great thanks again.

Answer 13

Since it's not, that implies it is "something else".
But yes, it turned out to be a polynomial in this case :) Since the exponent was a positive integer.