Could someone explain how to solve this math problem?

Question

I've graphed it, but I'm not sure how to solve the rest of the questions.

The National Oceanic and Atmospheric Administration (NOAA) has been measuring atmospheric
carbon dioxide concentations (in parts per million) at Mauna Loa, Hawaii since 1958. The data
closely follow the pattern H(t) = 0.013t2 + 0.81t + 316 + 3.5 sin 2πt, where t = 0 represents the
year 1960. (Complete dataset available at ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/c…

1. Explore the CO2 concentration model for the period 1960 – 1962.

a) Graph H for 0 ≤ t ≤ 3 and 300 ≤ H ≤ 340
b) Over the course of a single year, about how much does carbon dioxide concentration vary?
c) How much time is required for one complete cycle of carbon dioxide levels?
d) When during the year do the maximum and minimum occur?

Answer 1

NOTE - the formula should be:
H(t) = 0.013t^2 + 0.81t + 316 + 3.5 sin 2πt

Answer 2

since you have t^2 involved, the amount of variation depends on the year, but will always be roughly 2*3.5 = 7

since you have sin(2pi t) the period is 2pi/2pi = 1 year

max in April, min in Sep.

Don't know what graphing tool you use, but if you go to

http://rechneronline.de/function-graphs/

and enter

0.013x^2 + 0.81x + 316 + 3.5 *sin(2*pi*x)

for your function
with 0<=x<=5 and 300<=y<=350, the graph makes this quite clear.

Answer 3

how did you determine the maximum and the minimum?