Question

26) It has been observed that a particular plant's growth is directly proportional to time. It measured 2 cm when it arrived at the nursery and 2.5 cm exactly one week later. If the plant continues to grow at this rate, determine the function that represents the plant's growth.

Answer 1

The plant growth can be modelled by the function

$f(x)=mx+b$

where m is the rate of growth and b is the initial height of the plant.

We know that initially, the plant measured 2 cm; therefore, we can say b = 2. Hence, the equation now becomes

$f(x)=mx+2$

Now we just need to find m.

$m=\frac{\text{change in height}}{\text{time interval}}$$m=\frac{2.5\operatorname{cm}-2\operatorname{cm}}{1-0}=\frac{0.5\operatorname{cm}}{1}$

$\therefore m=0.5\text{ (cm/we}ek\text{)}$

Hence, the function that determines the plant growth is

$f(x)=0.5x+2$

which is our answer!