Jonathan has been on a diet since January 2013. So far, he has been losing weight at a steady rate. Based on monthly weigh-ins, his weight, \( w \), can be modeled by the function \( w = -3m + 205 \) where \( m \) is the number of months after January 2013.

a) How much did Jonathan weigh at the start of the diet?

b) How much weight has Jonathan been losing each month?

c) How many months did it take Jonathan to lose 45 pounds?

a ) w ( m ) = − 3 m + 205 m = 0 − a t t h e s t a r t o f t h e d i e t w ( 0 ) = − 3 ⋅ 0 + 205 = 205 A n s . w e i g h a t t h e s t a r t o f t h e d i e t i s 205 p o u n d s b ) w ( m + 1 ) = − 3 ( m + 1 ) + 2015 = − 3 m − 3 + 205 = − 3 m + 202 w ( m + 1 ) − w ( m ) = − 3 m + 202 − ( − 3 m + 205 ) = = − 3 m + 202 + 3 m − 205 = − 3 A n s . J o na t han ha s e a c h m o n t h 3 b ee n l os in g w ( m ) = 205 − 45 = 160 ⇒ − 3 m + 205 = 160 ⇒ \- 3 m = − 45 m = 15 A n s . 15 m o n t h

Answered by kate200468 | 2024-06-25

Jonathan weighed 205 pounds at the start of his diet and loses 3 pounds each month. It took him 15 months to lose 45 pounds. This is derived from the function modeling his weight loss over time.
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Answered by kate200468 | 2024-12-24