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
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Explanation:

Step1: Define variables

Let $h_0$ = initial height (when Vlad moved in), $h(t)$ = height after $t$ years, growth rate $r=26$ cm/year. The height formula is $h(t) = h_0 + rt$.

Step2: Solve for initial height

Substitute $t=4.5$, $h(4.5)=292$:
$292 = h_0 + 26\times4.5$
Calculate $26\times4.5=117$, so $h_0=292-117$

Step3: Calculate initial height

$h_0=175$

Step4: Solve for time at 357 cm

Substitute $h(t)=357$, $h_0=175$, $r=26$:
$357 = 175 + 26t$
Rearrange: $26t=357-175$

Step5: Calculate time $t$

$26t=182$, so $t=\frac{182}{26}=7$

Answer:

1. 175 centimeters
2. 7 years