y=18.47x - 2.96 / .24x+1 ,x> 0

Question

In photosynthesis, the amount of CO2 uptake (in milligrams per square decimeter per our) at optimal temperatures and with the natural supply of CO2 is approximated by y=18.47x - 2.96 / .24x+1 ,x> 0 where x is the light intensity (in watts per square meter). explain how to find the limiting amount of CO2 uptake and what it is.

Answer 1

Since CO2 uptake cant be negative I would just set the equation to 0 and solve for x which give you a x value of .16

Answer 2

This is a rational function where degree of the numerator equals the degree of the denominator.

As x->∞, y approaches 18.47/.24 (asymptotically.

See the following graph to get the idea:

desmos.com/calculator/c5jm58zqoc

To show how that limit is calculated divide all terms (numerator and denominator) by x.

y = (18.74 - 2.96/x) / (.24 + 1/x)

As x -> ∞, the terms with x in the denominator approach zero. So the limit is (18.74 - 0) / .24 + 0).