IA1.AT.C.12: Compare key properties (i.e., rates of change, intercepts, patterns of growth) of two functions, one linear and one exponential, when each is represented in a different way (i.e., algebraically, graphically, numerically in tables, or by narrative descriptions).

Compare key properties (i.e., rates of change, intercepts, patterns of growth) of two functions, one linear and one exponential, when each is represented in a different way (i.e., algebraically, graphically, numerically in tables, or by narrative descriptions).

Example Problems

A piston's vertical position (in cm) is

y(t)=4[-\sin((2\pi/0.04)t)] + 5

, where t is seconds.
What is the position at

t = 0.01

s?

The magnitude of a variable star is

M(t)=14.2 – 1.3 \cos[\frac{2\pi}{5.4}(t – 1.1)]

, with

t

in days.
What is its magnitude at

t = 3.8

days?

An EEG α‑wave signal is

B(t)=80 \\cos[2\\pi\\cdot10(t – 0.0125)]

µV, where t is in seconds. What is the phase shift expressed in milliseconds?

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