Question

Tara and Michelle are growing trees in their back yard. Tara's tree starts at a height of 10 feet, and grows 4 ft. a year. Michelle's tree starts at a height of 7 feet and grows 14% each year. How tall will Michelle's tree be after 12 years? When will Michelle's tree be taller than Tara's tree for the first time?

Answer 1

To determine the exponential growth of Michelle's tree at 12 years, taking into account that it measures 7 feet and grows 14% annually, the following calculation must be performed:

X = 7 x (1 + 0.14) 12

X = 33.7

Thus, in 12 years, the height of Michelle's tree will be 33.7 feet. In turn, the tree of Tara will measure 58 feet at the same time.

The first time Michelle's tree surpasses Tara's will be at age 20, when Michelle's tree will measure 96.2 feet (X = 7 x (1 + 0.14) 20), while Tara's tree will measure 90 feet.