Based on the the exponential growth function of Michelle's tree at 12 years, its height will be 33.7 feet.
At 20 years, Michelle's tree will surpass Tara's for the first time.
Exponential growth function:
y = ab^t
Where a is the initial value, b is the growth factor, and t is the time interval.
Michelle's Tree Exponential Growth Function:
Initial height = 7 feet
Growth rate = 14% each year
y = 7 x (1 + 0.14)^12
y = 33.7 feet
Tara's Tree Linear Growth Function:
Initial value = 10 feet
Growth rate = 4 feet per year
y = 10 + 4 x 12
y = 58 feet
The first time Michelle's tree surpasses Tara's will be at age 20, when Michelle's tree will measure 96.2 feet (y = 7 x (1 + 0.14)^20), while Tara's tree will measure 90 feet (10 + 40 x 20).
Thus, in 12 years, the height of Michelle's tree will be 33.7 feet whileTara will measure 58 feet.
Complete 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?