Question 1190085
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Write an exponential function in the form y=ab^x
that goes through points (0, 12) and (2,768)
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<pre>
In this problem, it is assumed that the parameter b is a positive real number.


First, the problem says that the plot of the function goes through point (0,12).


It means that the value of the function is 12 at x= 0.


So we write  12 = {{{a*b^0}}},  but since  {{{b^0}}} = 1 for any admittable value of b,

it implies that  a = 12.


Hence, we can write the function in the form  y = {{{12*b^x}}}.


Next, the problem says that the plot of the function goes through point (2,768).


It means that the value of the function is 768 at x= 2.


So we write  768 = {{{12*b^2}}}.


Dividing both sides by 12, we get  {{{b^2}}} = {{{768/12}}} = 64.

It implies that  b = {{{sqrt(64)}}} = 8  (we accept positive value of the square root, only).


Finally, the function is  y = {{{12*8^x}}}.


You may check, that this function satisfies the imposed conditions.
</pre>

Solved.