Answer:
17.25 years
Step-by-step explanation:
A certain type of conifer hedging increases in height by 17% each year for the first 20 years.When i bought some of this hedging, it was all about 50cm tall. How long will it take to grow 3m tall?
Step 1
We make sure all parameters have the same units, hence:
We convert 3m to cm
1 m = 100cm
3m = x
Cross Multiply
x = 3 × 100cm
x = 300cm
Step 2
To solve this question, we use the formula for Exponential growth =
y = a (1 + r) ^t
Where:
y = Size after time t = 3m = 300cm
a = Initial size of the tree = 20 cm
r = Growth rate = 17%
t = Time in years = ??
300 = 20 (1 + 0.17)^t
300 = 20(1.17) ^t
Divide both sides by 20
300/20 = 20(1.17) ^t/20
15 = 1.17^t
Take the Natural logarithm of both sides
In 15 = 1n 1.17^t
In 15 = t 1n 1.17
t = In 15/In 1.17
t = 17.248315544 years
Approximately = 17.25 years
