Question

When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard. He measured it once a year and found that it grew by 26 centimeters each year. 4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house? centimeters How many years passed from the time Vlad moved in until the tree was 357 centimeters tall? years

Answer 1

Answer:

The tree was 175 centimeters tall when Vlad moved into the house.

7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.

Step-by-step explanation:

The height of the tree, in centimeters, in t years after Vlad moved into the house is given by an equation in the following format:

$H(t) = H(0) + at$

In which H(0) is the height of the tree when Vlad moved into the house and a is the yearly increase.

He measured it once a year and found that it grew by 26 centimeters each year.

This means that $a = 26$

So

$H(t) = H(0) + 26t$

4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house?

This means that when t = 4.5, H(t) = 292. We use this to find H(0).

$H(t) = H(0) + 26t$

$292 = H(0) + 26*4.5$

$H(0) = 292 - 26*4.5$

$H(0) = 175$

The tree was 175 centimeters tall when Vlad moved into the house.

How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

This is t for which H(t) = 357. So

$H(t) = H(0) + 26t$

$H(t) = 175 + 26t$

$357 = 175 + 26t$

$26t = 182$

$t = \frac{182}{26}$

$t = 7$

7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.