A golf cart engine operates between $1,000$ to $3,000$ rpm$.$ Engine vibrations are transmitted at these frequencies to the cart chassis. They are measured by an accelerometer that outputs a corresponding voltage Ei from $1$ to $3$ V$.$ The voltage is digitized by an A$/$D converter with an analog input range of $0-5$ V$.$ a$)$ What is the recommended sampling frequency? b$)$ How many bits are needed for the worst$-$case relative quantization error to be better than $1\%?$ c$)$ How much memory is needed to record $10$ minutes of the signal?