Question

the graph shows an idealized description of the temperature (in °f) for approximately the last 150 thousand years of a location at the same latitude. complete parts (a)-(d). (a) find the highest and lowest temperatures recorded. the highest temperature is \\(\square\\)°f. the lowest temperature is \\(\square\\)°f. (b) use these two numbers to find the amplitude. the amplitude is \\(\square\\). (c) find the period of the function. the period is \\(\square\\) yr. (d) what is the trend of the temperature now? \\(\bigcirc\\) upward \\(\bigcirc\\) downward average annual temperature (idealized)

Explanation:

Step1: Find highest and lowest temp

From the graph, the peak (highest) is at 70°F, the trough (lowest) is at 40°F.

Step2: Calculate amplitude

Amplitude formula: $\frac{\text{Max}-\text{Min}}{2}$. So $\frac{70 - 40}{2}=\frac{30}{2}=15$.

Step3: Determine period

The distance between two consecutive troughs (e.g., 140,000 to 105,000 years ago) is $140000 - 105000 = 35000$ years.

Step4: Analyze current trend

Now is at 0 years ago (right end). The graph at the end is rising (from trough to peak), so trend is upward.

Answer:

(a) The highest temperature is $\boldsymbol{70}$°F. The lowest temperature is $\boldsymbol{40}$°F.
(b) The amplitude is $\boldsymbol{15}$.
(c) The period is $\boldsymbol{35000}$ yr.
(d) The trend of the temperature now is $\boldsymbol{\text{upward}}$.