1. First, we are going to find the value of
![x](https://tex.z-dn.net/?f=x)
form April. We know form our problem that <span> the maximum afternoon temperature in month, x, with x = 0 representing January, x = 1 representing February, and so on; therefore:
January </span>
![x=0](https://tex.z-dn.net/?f=x%3D0)
February
March
![x=2](https://tex.z-dn.net/?f=x%3D2)
April
![x=3](https://tex.z-dn.net/?f=x%3D3)
Now that we know that the value of
![x](https://tex.z-dn.net/?f=x)
that represent April is 3, we just need to replace
![x](https://tex.z-dn.net/?f=x)
with 3 in our model and evaluate:
![t=60-30cos( \frac{x \pi }{6} )](https://tex.z-dn.net/?f=t%3D60-30cos%28%20%5Cfrac%7Bx%20%5Cpi%20%7D%7B6%7D%20%29)
![t=60-30cos( \frac{3 \pi }{6} )](https://tex.z-dn.net/?f=t%3D60-30cos%28%20%5Cfrac%7B3%20%5Cpi%20%7D%7B6%7D%20%29)
![t=60-30(0)](https://tex.z-dn.net/?f=t%3D60-30%280%29)
We can conclude that the maximum temperature in April will be 60.2. Remember that in a function of the form
![y=C+Acos(Bx)](https://tex.z-dn.net/?f=y%3DC%2BAcos%28Bx%29)
![A](https://tex.z-dn.net/?f=A)
is the amplitude
![C](https://tex.z-dn.net/?f=C)
is the vertical shift
We have tow option to change our model to increase the maximum temperature to global warming:
1. Increase the value of D to increase the vertical shifting of the model. D affects the maximum value of the function; if we increase D, the maximum value of the function will increase as well. We know from our model that
![D=60](https://tex.z-dn.net/?f=D%3D60)
, so to increase the maximum temperature of our model, we just need to increase the value of 60.
2. Increase the value of A to increase the amplitude of the model. The amplitude, also increases or decreases the maximum value of the function -regardless of the sing of A, so if we increase the value of A, we will increase the value of the function. We know from our model that
![A=30](https://tex.z-dn.net/?f=A%3D30)
, so to increase the maximum temperature of our model, we just need to increase 30 (without considering the sign).