Atree grows 1 3/4 per year. how long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?

For this case, the first thing we must do is define variables.

We have then:

x: number of years

y: height of the tree in feet

We write the mixed numbers as decimals:

The expression that models the problem is:

By the time the tree reaches a height of 37 feet, we have:

From here, we uncover the number of years:

It will take the tree to grow from a height of 21 1/4 feet to a height of 37 feet about:

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.