00:01
In the given question we have to represent the exponential function, exponential function and we have to write the formula that represents y in terms of x, y in terms of x.
00:28
So we have given the first table is here we have the x value and here we have y x is negative 3 negative 2 negative 1 and y is given as 9 5 and 3 so let the exponential function be let the exponential function be y is equals to 8 times b to the power x we will take it as equation number a now substitute substitute the values of x and y in equation a from the given table so we have if we substitute the values we get y that is first is 9 is equal to a times b to the power negative 3 take it as equation 1 then we have 5 is equal to a times b to the power negative 2 then we have 3 is equal to 8 times v to the power negative 2 then we have 3 is negative 1 take it as equation number 3 now from second and third equation we have 5 over 3 if we divide this fourth equation we get b to the power negative 2 over b to the power negative 1 is equal to b over b square which is equal to 1 over b this gives us b is equal to 3 over 5 so we have 3 is equal to a times 5 over 3.
02:05
So this gives us a is equal to 9 over 5.
02:11
Therefore we have the formula is y is equal to a is 9 over 5 times we calculate b as 3 over 5 to the power x which is an given equation.
02:27
Now we have given the next table is with the values of x and y as 3 ,45, the values of x are 3, 4, 5 and y's values are 24, sorry, 2448 and 96.
02:47
Again we simplify it by considering the exponential function, y is equal to 8 times b to the power x.
02:55
So from given values we have 24 is equal to a times v to the power 3.
03:02
Take it as equation 1.
03:04
Then we have 48 is equal to a times v to the power 4 and we have 96 is equal to a times b to the power 5...