Polynomial praqctice help!!!

Question

The growth of the tree can be modeled by the function

h (t) = 3.3t - 0.54

Where h represents the height in metres and t represent time in years. Approximately how long will it take the tree to grow 32m tall?

a.) 105 years

b.) 5 years

c.) 19 years

d.) 10 years

Answer 1

There are a couple ways to solve this problem: one way is to find the time t algebraically, and another way is to plug in the given answer choices for t, and see which answer choice gives you a tree height h closest to 32m.

If we were to solve this problem algebraically:

h(t) = 3.3t - 0.54, where h(t) = h = 32, and t = ?

32 = 3.3t - 0.54

32.54 = 3.3t

If you could use a calculator, you get: 9.86 = t

Without a calculator, you can estimate the expression "32.54 = 3.3t" as: 33 = 3t

and get t = 11 approximately.

Which gives D) 10 years as the correct answer.

If we plugged in the answer choices to get a value for t:

We can first plug in choice D, t = 10 years, because it's easy to work with.

h(t) = 3.3(10) - 0.54

h(t) = 33 - 0.54

h(t) = 32.45

Which is very close to the desired height h of 32m, giving choice D as the correct answer.