Answered

A researcher in physiology has decided that a good mathematical model for the number of impulses fired after a nerve has been stimulated is given by ​y=x^2+50x-80, where y is the number of responses per millisecond and x is the number of milliseconds since the nerve was stimulated.
​(a)
When will the maximum firing rate be​ reached?
​(b)
What is the maximum firing​ rate?

Answer :

MRROYALGO

The maximum firing rate will be​ reached after 25 milliseconds and the maximum firing rate is 545 responses per millisecond

How to determine when the maximum firing rate will be​ reached?

From the question, we have the following parameters that can be used in our computation:

y = -x^2 + 50x - 80

Rewrite this function as

y = -x² + 50x - 80

Differentiate the function

So, we have

y = -2x + 50

Set to 0

-2x + 50 = 0

So, we have

2x = 50

Divide  by 2

x = 25

How to determine what the maximum firing​ rate is?

Recall that

y = -x² + 50x - 80

Also, we have

x = 25

So, we have

y = -(25)² + 50 x 25 - 80

Evaluate

y = 545

Hence, the maximum is 545 responses per millisecond

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