Question

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?

Answer 1

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