Question 1197241: A tree is 7 feet tall when it is planted write a formula for the height H(t) of the tree after t years if the tree grows 4 feet every year H(t)
Grows 4 feet every 5 years H(t)
Grows 1 foot every 5 years H(t)
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
| Rate | Formula | | Grows 4 feet every year | H(t) = 4t+7 | | Grows 4 feet every 5 years | H(t) = (4/5)t+7 | | Grows 1 foot every 5 years | H(t) = (1/5)t+7 |
Side note: 4/5 = 0.8 and 1/5 = 0.2
Each equation is of the form y = mx+b
y = H(t) = height at time t
m = slope = tells us how fast the tree is growing
x = t = input time value, in years
b = starting height = 7 for each equation
If a tree grows 4 feet every 5 years, then it grows 1 foot every 4/5 = 0.8 years.
If needed, we can make a table of values.
Here's a sample table for the third formula
| t | H(t) = (1/5)t+7 | | 0 | 7 | | 1 | 7.2 | | 2 | 7.4 | | 3 | 7.6 | | 4 | 7.8 | | 5 | 8 | | 6 | 8.2 | | 7 | 8.4 | | 8 | 8.6 | | 9 | 8.8 | | 10 | 9 |
Each time we reach a multiple of 5, we get to another whole number for H(t)
In other words
t = 0 leads to H(t) = 7
t = 5 leads to H(t) = 8
t = 10 leads to H(t) = 9
I'll let you generate the other tables if your teacher requires it.
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