Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 20)(0,20) and (6, 1280)(6,1280).

Answer 1

Answer:

$y=20(2)^x$

Step-by-step explanation:

We want to write an exponential function that goes through the points (0, 20) and (6, 1280).

The standard exponential function is given by:

$y=ab^x$

The point (0, 20) tells us that y = 20 when x = 0. Hence:

$20=a(b)^0$

Simplify:

$20=a(1)\Rightarrow a=20$

So, our exponential function is now:

$y=20(b)^x$

Next, the point (6, 1280) tells us that y = 1280 when x = 6. Thus:

$1280=20(b)^6$

Solve for b. Divide both sides by 20:

$64=b^6$

Therefore:

$b=\sqrt[6]{64}=2$

Hence, our function is:

$y=20(2)^x$