Question

20 POINTS AND BRAINLIEST!! Write an exponential function in the form y=ab^x
that goes through points (0, 13) and (3,832).

Answer 1

Answer:

$y=13(4)^x$

Step-by-step explanation:

We have the exponential function of the form:

$y=ab^x$

And it goes through the points (0, 13) and (3, 832).

Hence, when we substitute in 0 for x, we should get 13 for y. Therefore:

$13=ab^0$

Since anything to the zeroth power is 1, this yields:

$a=13$

So, we determined that the value of a is 13.

So, our function is now:

$y=13b^x$

We will need to determine b. We know that y equals 832 when x is 3. Hence:

$832=13(b)^3$

Divide both sides by 13:

$b^3=64$

Take the cube root of both sides:

$b=4$

Hence, our b value is 4.

Therefore, our entire equation is:

$y=13(4)^x$