Question

The temperature of a chemical reaction ranges between 40°C and 180°C. The temperature is at its lowest point when t = 0 and completes one cycle over a 12-hour period. What is a sine function that would model this reaction?

Here's the answers:

http://prntscr.com/410g9j

I think it's C because I know the period b is pi/6, but I don't know if it's D or not because the midline and amplitude thing can both have a range between 40 and 180. Please help?

Answer 1

@mathmale can you help me please?

Answer 2

@amistre64

Answer 3

Actually, the period is 12 hours. Look at that problem statement again: "... completes one cycle over a 12-hour period."

Here the relevant sinusoidal model is y=a*sin (b*x). The relationship between the period and the coefficient 'b' (which is not the period, by the way) is \[period=\frac{ 2\pi }{ b }\]

Answer 4

Your job is to find b, given the period (which is 12 hours).

Answer 5

I meant that the "b" in the sine equation should be pi/6.

Answer 6

Think: We are to determine a sine function model. Normally, the sine function ranges from -1 to +1. In this problem it ranges from 40 to 180 degrees Celcius, so we know that there must be an offset (that raises the graph above the horizontal axis).

An appropriate model is thus

\[y = a*\sin bx+c\] where 'c' represents that offset. To find the offset (c), find the average of 40 and 180 degrees.

What else do you need to know to solve this problem?

Answer 7

I feel like C or D could be the answer, because if the midline is at 70 with an amplitude of 110 it could fulfill 40-180. And if the midline's at 110 with an amplitude of 70 it could too.

Answer 8

But if t=0, wouldn't the value be 110 for C and 70 for D? It says that it has to equal 40?