Respuesta :
If a quantity A is decreased by 15%, it means that what is left is 85% of it.
85%A=[tex] \frac{85}{100}A=0.85A [/tex]
Part A.
Consider the 150 marigolds.
After the first month, 0.85*150 are left
After the second month, 0.85*0.85*150=[tex] (0.85)^{2} *150[/tex]
After the third month, 0.85*0.85*0.85*150 = [tex] (0.85)^{3}*150 [/tex]
.
.
so After n months, [tex] (0.85)^{n}*150 [/tex] marigolds are left.
in functional notation: [tex]M(n)=(0.85)^{n}*150[/tex] is the function which gives the number of marigolds after n months
consider the 125 sunflowers.
After 1 month, 125-8 are left
After 2 months, 125-8*2 are left
After 3 months, 125-8*3 are left
.
.
After n months, 125-8*n sunflowers are left.
In functional notation: S(n)=125-8*n is the function which gives the number of sunflowers left after n months
Part B.
[tex]M(3)=(0.85)^{3}*150=0.522*150=78[/tex] marigolds are left after 3 months.
S(3)=125-8*3=125-24=121 sunflowers are left after 3 months.
Part C.
Answer : equalizing M(n) to S(n) produces an equation which is very complicated to solve algebraically.
A much better approach is to graph both functions and see where they intersect.
Another approach is by trial, which gives 14 months
[tex]M(14)=(0.85)^{14}*150=15[/tex]
[tex]S(14)=125-8*14=125-112=13[/tex]
which are close numbers to each other.
85%A=[tex] \frac{85}{100}A=0.85A [/tex]
Part A.
Consider the 150 marigolds.
After the first month, 0.85*150 are left
After the second month, 0.85*0.85*150=[tex] (0.85)^{2} *150[/tex]
After the third month, 0.85*0.85*0.85*150 = [tex] (0.85)^{3}*150 [/tex]
.
.
so After n months, [tex] (0.85)^{n}*150 [/tex] marigolds are left.
in functional notation: [tex]M(n)=(0.85)^{n}*150[/tex] is the function which gives the number of marigolds after n months
consider the 125 sunflowers.
After 1 month, 125-8 are left
After 2 months, 125-8*2 are left
After 3 months, 125-8*3 are left
.
.
After n months, 125-8*n sunflowers are left.
In functional notation: S(n)=125-8*n is the function which gives the number of sunflowers left after n months
Part B.
[tex]M(3)=(0.85)^{3}*150=0.522*150=78[/tex] marigolds are left after 3 months.
S(3)=125-8*3=125-24=121 sunflowers are left after 3 months.
Part C.
Answer : equalizing M(n) to S(n) produces an equation which is very complicated to solve algebraically.
A much better approach is to graph both functions and see where they intersect.
Another approach is by trial, which gives 14 months
[tex]M(14)=(0.85)^{14}*150=15[/tex]
[tex]S(14)=125-8*14=125-112=13[/tex]
which are close numbers to each other.
