Question 152269
The starting height is 8 cm, so this means that the constant of the equation {{{y=mx+b}}} is 8. This means that {{{b=8}}}. Since it "is growing at a rate of 4/5 cm per week", the slope is {{{m=4/5}}}. So the entire equation is 


{{{y=(4/5)x+8}}}



Now convert {{{13&3/5}}} to an improper fraction



{{{13&3/5=(13*5+3)/5=(65+3)/5=68/5}}}



{{{y=(4/5)x+8}}} Start with the given equation.



{{{68/5=(4/5)x+8}}} Plug in {{{y=68/5}}}. This is the same as {{{y=13&3/5}}}



{{{68/5-8=(4/5)x}}} Subtract 8 from both sides.



{{{28/5=(4/5)x}}} Combine like terms



{{{7=x}}} Multiply both sides by {{{5/4}}} to isolate x.



So the answer is {{{x=7}}} which means that it will take 7 weeks for the plant to reach (and exceed) a height of {{{13&3/5}}} cm.