Example 2: Weight Changes

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Problem. As a New Year's resolution, Josh decides to lose some weight. On January 1, he steps on the scale to record his initial weight value:  J(0) = 327 lb. He then begins a regular exercise program and eliminates all snack foods from his diet. Ten days later he triumphantly steps back on the scale to measure a new value:  J(10) = 324 lb. At what rate is Josh losing weight?

Solution. Over the first ten days of the new year, the change in value of Josh's weight is given by  DJ = 324 – 327 = –3 lb. The negative sign indicates that his weight has indeed decreased.

Since this decrease has taken place over an interval of  Dt = 10 – 0 = 10 days, he has been losing weight at a rate of  DJ/Dt = –3/10  of a lb. per day. This rate may increase or decrease over the next  Dt = ten days, depending on whether Josh increases or decreases the size of his ...change in value.