Question

A stalacite grows according to the formula L(t)=17.75 + 1/250t, where L(t) represents the length of the stalacite, in inches, and t represents the time in years, since 1970. Find the vertical intercept and the slope and explain their meaning.

(basic linear function problem)

Answer 1

The given formula for the growth of a stalactite is L(t) = 17.75 + (1/250)t. This is a linear function, where L(t) represents the length of the stalactite in inches at a given time t, measured in years since 1970.

In a linear function of the form y = mx + b:

- The coefficient m represents the slope, which is the rate of change of y with respect to x.
- The constant term b represents the y-intercept, which is the value of y when x is 0.

For the stalactite function L(t) = 17.75 + (1/250)t:

1. The vertical intercept (y-intercept) is 17.75 because this is the constant term in the equation. It represents the length of the stalactite in the year 1970, which is the starting point of our time measurement (when t = 0).

2. The slope is 1/250 because this is the coefficient of the t variable in the equation. It represents the growth rate of the stalactite. Specifically, it says that for every year that passes, the stalactite grows by 1/250 inches.

To summarize:

- The vertical intercept is 17.75 inches, which is the initial length of the stalactite in 1970.
- The slope is 1/250 inches per year, which indicates the stalactite grows at a rate of 1/250 inches every year.

Answer 2

The vertical intercept is 17.75 and is the value when t=0. The vertical intercept is the height in inches of the stalactite in inches in 1970.

The slope is 1/250 and is how much it is growing in inches per year ( since t is in years)

Explanation:

L(t) = 1/250 *t +17.75

This is in the form y= mx+b where m is the slope and b is the y intercept

The vertical intercept is 17.75 and is the value when t=0. The vertical intercept is the height in inches of the stalactite in inches in 1970.

The slope is 1/250 and is how much it is growing in inches per year ( since t is in years)