Question

There are 10 coconuts at-the base of your tree. The coconuts are falling off the tree at a rate of 6 coconuts per week. Assume that you do not pick up any coconuts. a. Write and graph a linear equation that represents the number of coconuts at the base of your tree after x weeks.
a. Write and graph a linear equation that represents the number of coconuts at the base of your tree after x weeks.

b. The tree will have no coconuts on it when there are 52 coconuts at the base of the tree. After how many weeks will this occur?

Answer 1

Answer: y = 6x +10.

After 7 weeks there will not be any coconut on the tree.

Step-by-step explanation: Given initial number of coconuts under the tree = 10 coconuts.

The rate of falling of coconuts each week = 6 coconuts per week.

Let us assume number of weeks be x and y be total number of coconuts after x weeks.

So, total number of coconuts after x weeks would be = Rate of falling of coconuts × number of weeks + Initial number of coconuts.

Therefore,

y = 6x +10.

a) y = 6x +10

Let us graph the linear equation with y-intercept 10 and slope rise/run = 6/1.

b) Total number of coconuts after x weeks = 52.

Plugging y=52 in above equation, we get

52 = 6x+10.

Subtracting 10 from both sides, we get

52-10 = 6x=10-10

42 = 6x.

Dividing both sides by 6, we get

42/6 = 6x/6

7 = x.

Therefore, after 7 weeks there will not be any coconut on the tree.