i need help with math help

Question

find the exponential function in form y=ab^x that pass thru point (1,12) and (3,48)

Answer 1

Find the exponential function f(x) = ab^x that passes through (1,12) and (3,48).

To do this, we first plug in the x- and y-values:

12 = ab¹ <--> ab = 12

48 = ab³ <--> ab³ = 48

Now, we must proceed to solve for a and b. This requires some brainstorming. Notice that 48 = 12 x 4. So, if we multiply the first equation (ab = 12) by 4, we get the second equation:

4ab = 48

ab³ = 48

So, 4ab = ab³ , and dividing both sides by ab yields 4 = b². Therefore b = ± 2. Exponential functions must have a positive base. So b = 2. Our function is now

f(x) = a · 2^x

Since, ab = 12 and b = 2, we must have a = 6. Therefore, our final answer is

f(x) = 6 · 2^x.