Construction of the Tower of Pisa was completed in 1360. By 1990, the tilt of the tower was so severe that it was closed for renovation. Renovators were able to reduce the tower's 1990 tilt by 17 inches. The resultant tower leans 13.5 feet (162 inches) off the perpendicular. When the tower was reopened in 2001, officials forecast that it would take 300 years for the tower to return to its 1990 tilt.

(a) Construct a linear formula that models the lean of the renovated tower, where l is the number of inches from the perpendicular and t is the number of years since 2001.

The formula is: 162 + (17/300) t

Use the formula from part (a) to predict the lean of the tower in 2150. (Round your answer to two decimal places.

(a) The linear formula that models the lean of the renovated tower is:

I = (17 / 300) t + 162

In 2150, the tower will lean 170.44 inches off the perpendicular.

Step-by-step explanation:

dа ta:

Renovators were able to reduce the tower's 1990 tilt by 17 inches. The resultant tower leans 162 inches off the perpendicular. In 2001, officials forecast that it would take 300 years for the tower to return to its 1990 tilt.

(a)

A linear formula has the form:

y = mx + b

where

y is the dependent variable x is the independent variable m is the slope, and b is the y-axis interception

In this case, the dependent variable is the tilt of the tower, measured as the number of inches from the perpendicular. Let's call "I" this variable. And what does it depend on? It depends on the variable time. The tilt of the tower varies over time.

Therefore, the time (in years) is the independent variable. Let's call "t" this variable.

The slope (m) is the change in the dependent variable for each unit of the independent variable. So, it is the change in the number of inches from the perpendicular, for each year elapsed.

Officials forecast that it would take 300 years for the tower to return to its 1990 tilt. In other words, 300 years to the tower to lean 17 inches. Or, the tower will lean 17 inches in 300 years. That is the slope (m).

m = (17 / 300) inches per year

The y-axis interception (b) is the value of the dependent variable (I) when the independent variable (t) is equal to zero.

Our t=0 occurs when the tower was reopened, in 2001.

At that time, the tower leaned 162 inches off the perpendicular.

b = 162

Then, the linear formula that models the lean of the renovated tower is:

I = (17 / 300) t + 162

or

I = 162 + (17 / 300) t

To predict the lean of the tower in 2150, let's substitute the independent variable t in the formula for the time elapsed from 2001 (our t=0) to 2150.

Time elapsed = 2150 - 2001 = 149 years

I = 162 + (17 / 300) * 149

I = 170.44

In 2150, the tower will lean 170.44 inches off the perpendicular.