The students in lab derived a function to model the results of their experiment on the effect of heat on a chemical where x represents the number of minutes heat was applied at a constant temperature.

Question

In a chemistry class, the students in lab derived a function to model the results of their experiment on the effect of heat on a chemical where x represents the number of minutes

heat was applied at a constant temperature set by the lab instructions. Their function was . The teacher said the function should have been  .

a) Was there ever any time at which these two functions were the same. If so, when?

b) For what values of x is their derived function greater than the actual function?

*NOTE*

Grade 12 Advanced Functions (MHF4U)

Please answer clearly and neatly.

Thanks

Answer 1

This is easier visualized if you plot both functions.

The domain of the function is [0, ∞).

Set the two equations equal to each other and solve for x to find when the two functions are equal. Ignore any negative results.

You can see from the plots that their function is greater on the interval (x, ∞). Both functions will eventually

tend to zero.