Calculus I - Week 02 Written HW

01

Solve trig equation using trig identities

Find all values of $x\in [0,2\pi ]$ such that $\sin 2x=\sin x$.

(Hint: double angle formula.)

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02

Related rates - balloon volume and radius

Suppose a balloon maintains a spherical shape while it is inflated. Suppose its radius is increasing at a rate of $4cm/s$.

• (a) Write the balloon’s radius as a function of time $t$.
• (b) Write the balloon’s volume as a function of time $t$.

Interpret your answer.

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03

Determining exponential parameters from points on graph

Find the constant parameters $C$ and $b$ for which the exponential function $f(x)=C{b}^x$ has the following graph:

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