 Hello and welcome to the session. In this session we will discuss a question with Cesar. The table below shows the values of an exponential function. Find the equation of this exponential function. Now in this input output table, the values of x are given as 0, 5, 10 and 15. And the corresponding values of y are given as 6, 12, 24 and 48. Now before starting the solution of this question, we should know a result. And that is an exponential function is the function that can be described by an equation of the form y is equal to a into b raised to power x where a is not equal to 0, b is greater than 0 and b is not equal to 1. Also a and b are constants. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Here we will construct the exponential function from an input output table where the values of x are called input values and the values of y are called output values. And here we are given this input output table. So we have to construct an exponential function from this table. Now from the key idea we know that an exponential function is of the form y is equal to a into b raised to power x. So here first of all we will find the values of a and b. Now let this be equation number one. Now from the table we can see that when x is equal to 0, y is equal to 6. So here we are given a point that coordinates 0, 6. So let us put x is equal to 0 and y is equal to 6 in equation one. So here we have 6 is equal to a into b raised to power 0 which implies 6 is equal to a into. Now b raised to power 0 will be 1. So this will be 6 is equal to a or we can write it as a is equal to 6. So we have found the value of a. Now let us find the value of b from this table. For this we see ratio of the negative values of y. Now here we see 12 upon 6 is equal to 2. Then 24 upon 12 is also 2. And then 48 upon 24 is again 2. So here we are getting a constant factor and this constant factor is 2. But see the difference in the intervals of x. Here you can see 5 minus 0 is equal to 5. Then 10 minus 5 is equal to 5. And 15 minus 10 is equal to 5. So difference in the intervals of x is 5. So the values are increasing by constant factor 2 over the equal interval of 5. So b is equal to 2 raised to power 1 upon 5. Now we will put the values of a and b in this equation. And we have y is equal to 6 into 2 raised to power 1 upon 5 whole raised to power x. And this is the required exponential function. So from this input output table we have obtained this exponential function. Now you can also find the value of b by putting any other pair from this input output table in this equation. Now let us put the ordered pair 10, 24 in y is equal to a into b raised to power x. This means we will put x is equal to 10 and y is equal to 24 in this equation. So we have 24 is equal to a into b raised to power 10. Now we have already obtained the value of a. So we will put a is equal to 6 in this equation. And we have 24 is equal to 6 into b raised to power 10. Which implies 24 upon 6 is equal to b raised to power 10. Which implies 4 is equal to b raised to power 10. Now taking positive 10th root on both sides we get 4 raised to power 1 upon 10 is equal to b raised to power 10. Whole raised to power 1 upon 10. This implies now 4 can be written as 2 raised to power 2. So here we will write 2 raised to power 2 whole raised to power 1 upon 10 is equal to b raised to power 10 whole raised to power 1 upon 10. Now this implies 2 raised to power 2 into 1 upon 10 is equal to b raised to power 10 into 1 upon 10. So simplified exponents we have 2 raised to power 1 upon 5 is equal to b raised to power 1. And this implies b is equal to 2 raised to power 1 upon 5. So we have found the value of b by putting any other pair from the given table. So putting the values of a and b in this equation we get y is equal to 6 into 2 raised to power 1 upon 5 whole raised to power x. And this is the required exponential function. So this is the solution of the given question. That's all for this session. Hope you all have enjoyed the session.