Question

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The following chart shows Peter's monthly electricity usage (in kWh).
Find a function to model the data. (Estimate the values given in the chart to a multiple of 25, and set January at t=0)
E(t)=
The link for this graph
https://api.agilixbuzz.com/Resz/~0.74QNeMFvrichWLKH.PJXjwGodOZLtToelsbWjnqGHv9nuADk3w1AE8HXr22o/57829733,B7B,7/Assets/Media/Images/2c-Bank-Chart-01e.jpg

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} t & 1&3&4&5&7&9&10&11 \\ \hline E(t) & 175&350&525&700&875&700&525&350 \\ \end{array}$$

$$A={875-175 \over 2}=350$$

$$T=12, k={2\pi \over T}={2\pi \over 12}={\pi \over 6}$$

$$175+350=525$$

$$E(t)=525-350\sin({\pi \over 6}(t+2))$$

$$E(t)=525-350\sin({\pi \over 6}t+{\pi \over 3})$$

January:t=0

$$E(t)=525-350\sin(0+{\pi \over 3})=525-175\sqrt{3}\approx221.891\ kWh$$