C2 question. pretty urgent.

A shrub is planted when it is 2m tall. In the nth year after planting, the shrub grows by hn m where
h_n+1 = 0.8 x h_n One year after planting, it is 2.3 m tall.

Find the height of the shrub after 10 years
Show that the shrub will never grow more than 3.5 m in height

thanks a lot. I'm having difficulty working out the nth term.

Reply 1

7589200

18

It is a Geometric Progression.

Ok, in the first year, there has been 0.3m of growth. So a = 0.3. To get every next term, you just times by 0.8, so r = 0.8.

After 10 years, you need to sum the growth for that many years and add it to the original value.

Sn = a(1-r^n)/(1-r) = 0.3(1-0.8^10)/0.2 = 1.33

(It equals 1.33m - so its 2 + 1.33m to get the answer)

To prove that, you need to sum to infinity and make sure that its 1.5m ( 3.5 - 2). (and this does equal 1.5m exactly)

S(infinity) = a/(1 - r) = 0.3 / 0.2 = 1.5

Reply 2

icecreamman

OP

1

where does the 0.8 come in?

--------------

Vazzyb

It is a Geometric Progression.

I know that. how do you do it though?

Reply 3

Robob

17

use the formula for the sum of a geometric progression to find the height after 10 years

use the formula for the sum to infinity to show that it will never excede 3.5m in height

--------------

a=0.3
r=0.8
n=10

sub into forumla for sum then add 2m

then use formula for sum to infinity and add 2m again, should equal 3.5m

Reply 4

icecreamman

OP

1

rpotter

use the formula for the sum of a geometric progression to find the height after 10 years

use the formula for the sum to infinity to show that it will never excede 3.5m in height

--------------

a=0.3
r=0.8
n=10

sub into forumla for sum then add 2m

then use formula for sum to infinity and add 2m again, should equal 3.5m