Hi everyone could someone help me to resolve this ?

It has been observed that a particular plant's growth is a linear function of time. The plant measured 2cm when it arrived at the nursery, and 5cm two weeks later.

1. If the plant continues to grow at thiss rate, determine the linear function that represents the plant's. Let T be the time since the plant arrived at the nursery in weeks, and G(t) be the measurement of the plants in cm.

2. What will the plant measure in 3 months ??

Best and Thank you !

Thalys

Thalys
Nov 2, 2015

#1**+10 **

Let t be the time elapsed since it arrived at the nursery and let g be the height at any time, t.

Notice....at t = 0, h = 2 cm = ( 0, 2)

And at t = 2, h = 5 = (2, 5)

So.....to get a linear equation, we first need to find the slope.....so we have

[ 5 - 2 ] / [ 2 - 0 ] = 3/2 and using (0, 2) we have

y - 2 = (3/2) (x - 0)

y = (3/2)x + 2 and we can this linear function as :

g(t) = (3/2)t + 2

(2) 3 months = 12 weeks....so we have

g(12) = (3/2) (12) + 2 = 18 + 2 = 20 cm

CPhill
Nov 2, 2015

#1**+10 **

Best Answer

Let t be the time elapsed since it arrived at the nursery and let g be the height at any time, t.

Notice....at t = 0, h = 2 cm = ( 0, 2)

And at t = 2, h = 5 = (2, 5)

So.....to get a linear equation, we first need to find the slope.....so we have

[ 5 - 2 ] / [ 2 - 0 ] = 3/2 and using (0, 2) we have

y - 2 = (3/2) (x - 0)

y = (3/2)x + 2 and we can this linear function as :

g(t) = (3/2)t + 2

(2) 3 months = 12 weeks....so we have

g(12) = (3/2) (12) + 2 = 18 + 2 = 20 cm

CPhill
Nov 2, 2015