<h2>
Answer:</h2>
Hence, the cost for 6 calculators is:
$ 133
<h2>
Step-by-step explanation:</h2>
Let it follows the quadratic model.
i.e let
where a,b and c are real numbers.
where p(x) denotes the cost of x calculators.
Now, it is given that:
The company discovered that it costs $61 to produce 3 calculators.
i.e. when x=3 p(x)=61
Hence, we get:
and cost of 7 calculators is: $ 165
i.e.
and cost of 12 calculators is: $385
i.e.
on subtracting equation (2) from (1) we get:
on dividing both side by 4 we get:
on subtracting equation (3) from equation (2) and dividing by 5 we get:
Now on subtracting equation (4) from (5) we get:
and by putting the value of a in equation (4) we get:
and now putting the value of a and b in equation (1) we get:
Hence, the function that models the cost is:
Now, we are asked to find the cost of 6 calculators
when x=6 we have:
The cost of 6 calculators is:
$ 133