 Hello and welcome to the session. In this session we will discuss the question which says that Sam says that the values of the function f of x is equal to 7 raised to power x will increase faster than the values of the function g of x is equal to 7x. Do you agree or disagree with Sam? Justify your answer. Now let us start with the solution of the given question. Here Sam says that the values of the function f of x is equal to 7 raised to power x will increase faster than the values of the function g of x is equal to 7x. Now let us first construct the input output table for the two functions. Now when x is 0 then f of x is equal to 7 raised to power 0 that is equal to 1 and g of x is equal to 7 into 0 that is 0. Now when x is equal to 1 f of x is equal to 7 raised to power 1 that is 7 and g of x is equal to 7 into 1 that is again 7. Now when x is equal to 2 f of x is equal to 7 raised to power 2 that is 7 into 7 which is equal to 49 and g of x is equal to 7 into 2 that is 14. Now when x is equal to 3 f of x is equal to 7 raised to power 3 which is equal to 7 into 7 into 7 that is 343 and g of x is equal to 7 into 3 that is 21. Now when x is equal to 4 f of x is equal to 7 raised to power 4 that is equal to 2401 and g of x is equal to 7 into 4 that is equal to 28. So this is the required input output table. Now for the function g of x is equal to 7x let us see the pattern. Now here you can see values of g of x are increasing by a difference as x increases by 1 in an additive pattern now here you can see 7 then 7 plus 7 is 14 then 7 plus 7 plus 7 is 21 then 7 plus 7 plus 7 plus 7 is 28. So this is the additive pattern so it is a linear function. Now for the function f of x is equal to 7 raised to power x the values of f of x are increasing at a very high rate then the values of g of x they are following the multiplicative pattern as x is increased by 1 now here you can see 7 then 7 into 7 is 49 then 7 into 7 into 7 is 343 and then 7 into 7 into 7 into 7 is 2401 so it is an exponential function. Also you can see when x is 3 the value given by linear equation is 21 but the value given by the exponential equation is 343. Thus we see that the values increasing exponentially are faster than the values increasing linearly thus some scale is correct and we agree with this conclusion. So this is the solution of the given question that's all for this session hope you all have enjoyed the session.