SOLUTION: Every year, a tree bears 3 more fruits than it did the previous year. If it bore 12 fruits in 1995, how many fruits would it bear by 2010?

Question 1119942: Every year, a tree bears 3 more fruits than it did the previous year. If it bore 12 fruits in 1995, how many fruits would it bear by 2010?
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Every year, a tree bears 3 more fruits than it did the previous year. If it bore 12 fruits in 1995, how many fruits would it bear by 2010?
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2010 - 1995 = 15 years
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12 + 3*15 = 57
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it bears 3 more fruits every year.

it bore 12 in 1995.

how many will it bear in 2010.

2010 - 1995 = 15 years.

15 * 3 = 45

it will bear 12 + 45 = 57 fruits in 2010.

if you let x equal the number of years, then your equation becomes:

y = 3x + 12

if you let 1995 represent year 0, then 2010 will represent year 15 because 1995 + 15 = 2010.

basically, you just add 1995 to x to find the year that it represents.

x = 0, the year is 1995.
x = 15, the year is 1995 + 15 = 2010.

you can graph the equation of y = 3x + 12.

it looks like this:

you can also let x represent the year, although this equation is a littler more cumbersome to graph and represent.

in that case, the equation becomes y = 3 * (x - 1995) + 12

that graph looks like this:

what you have done is shifted the graph horizontally 1995 units to the right.

when x is 1995, (x-1995) is equal to 0.

the equation then becomes y = 0 + 12 which results in y = 12.

when x is 2010, (x-1995) is equal to 15.

the equation then becomes y = 3 * 15 + 12 which results in y = 57.

both forms get you the same value of y.

the fact that you have the same increase year makes the equation a linear equation of the form y = mx + b.

m is the slope.
b is the y-intercept.

the slope is 3 in both equations because the increase is 3 units each year.

the y-intercept in the first equation is found by making x = 0 and solving for y.

y = 3x + 15 results in y = 15 when x = 0.

that's the y-intercept for the first equation.

the y-intercept for the second equation is found the same way.

y = 3 * (x - 1995) + 12 results in y = 3 * -1995) + 12 which results in y = -5973 when x = 0.

that's the y-intercept in the second equation.

the first form of the equation is the preferred form, although the second form is still valid.

here's the graph of the y-intercept of the first equation.

here's the graph of the y-intercept of the second equation.

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