An overweight man makes lifestyle changes in order to lose weight. His starting weight is 290 pounds and he has set a target weight of 200 pounds. Let t be the time (in months), and let D be the difference (in pounds) between his weight at time t and his target weight. Each month the difference D decreases by 15%.
(a) Make an exponential model of D versus the time t in months since the diet began.
D(t) =
(b) How long will it take for his weight to reach 220 pounds? (Round your answer to two decimal places.)
months
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D(t) = 290 * 0.85^t
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