Question

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 month did it take Jonathan to lose 45 pounds?

Show work plz

Answer 1

$a)\ \ \ w(m)=-3m+205\\\\m=0\ \ \ - at\ the\ start\ of\ the\ diet\\ \\w(0)=-3\cdot0+205=205\\ \\Ans.\ weigh\ at\ the\ start\ of\ the\ diet\ is\ 205\ pounds\\ \\b)\ \ \ w(m+1)=-3(m+1)+2015=-3m-3+205=-3m+202\\ \\w(m+1)-w(m)=-3m+202-(-3m+205)=\\ \\=-3m+202+3m-205=-3\\ \\Ans.\ Jonathan\ has\ each\ month\ 3\ been\ losing \\ \\ w(m)=205-45=160\ \ \ \Rightarrow\ \ \ -3m+205=160\ \ \ \Rightarrow\ \ \-3m=-45\\ \\m=15\\ \\Ans.\ 15\ month$