Gilberto plants two trees in his front yard. The apple tree is three feet tall and will grow 20 percent taller each year. The olive tree is two feet tall and will grow 30 percent taller each yearCreate equations that model each tree's height per yearHow many years will it take for the trees to reach the same height? (1 point) approximately 42 years approximately 5 years approximately years approximately 7 years
Let A(t) represent the height of the apple tree after t years. Since it grows 20% taller each year, the equation would be:
A(t) = 3 * (1 + 0.20)^t
Let O(t) represent the height of the olive tree after t years. Since it grows 30% taller each year, the equation would be:
O(t) = 2 * (1 + 0.30)^t
To find out how many years it will take for the trees to reach the same height, we need to set the two equations equal to each other:
3 * (1 + 0.20)^t = 2 * (1 + 0.30)^t
Solving for t gives:
(1.20)^t = (1.30)^t
1.20t = 1.30t
t = log(1.30)/log(1.20)
t = 41.95
Therefore, it will take approximately 42 years for the trees to reach the same height.