Question

Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in. H=210+33t. How fast does the tree grow?

Answer 1

Given:

In equation H=210+33 t where H represents the height of the tree (in centimetres ) and t represent in years.

To Find:

How fast does the tree grow?

Solution:

In given equation, we see that:

t is independent variable and H is dependent variable:

So we put value of t in terms of years like 1,2,3,4,....   in given equation:

$\mathbf{H= 210 +33\times t}$

For t = 1

$\mathbf{H_{1}= 210 +33\times 1= 210 + 33 = 243 \ cm}$

For t = 2

$\mathbf{H_{2}= 210 +33\times 2= 210 + 66 = 276\ cm}$

For t = 3

$\mathbf{H_{3}= 210 +33\times 3= 210 + 99 = 309\ cm}$

For t = 4

$\mathbf{H_{4}= 210 +33\times 4= 210 + 132 = 342\ cm}$

.

.

.

Here we see that height of tree in successive year is:

243 , 276, 309, 342 ....

Difference between two consecutive year is:

Difference = 276 - 243 = 33

We see that difference between height of consecutive years is same. That consecutive difference is 33.

Means height of tree every year increase by 33 cm. So series of height of tree is in arithmetic progression series.

Answer 2

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• Difference between two consecutive year is:

• Difference = 276 - 243 = 33

• Height of tree every year increase by 33 cm. So series of height of tree is in arithmetic progression series.