Math Problem Statement

How many inches of snow are on the ground at midnight? How do you know?

Solution

The equation modeling the height of snow on Jasper's driveway is given by:

f(x)=5+23xf(x) = 5 + \frac{2}{3}x

where f(x)f(x) is the height of the snow in inches, and xx is the number of hours after midnight.

To find how many inches of snow are on the ground at midnight, we substitute x=0x = 0 (since x=0x = 0 represents midnight) into the equation:

f(0)=5+230=5f(0) = 5 + \frac{2}{3} \cdot 0 = 5

So, there are 5 inches of snow on the ground at midnight.

Would you like more details or have any other questions?

Here are some related questions for further exploration:

  1. How much snow will accumulate after 6 hours?
  2. What is the rate at which snow is accumulating per hour?
  3. After how many hours will there be 11 inches of snow on the ground?
  4. What is the meaning of the constant 5 in the equation?
  5. If the rate of snow accumulation doubled, how would the equation change?

Tip: The constant term in a linear equation often represents an initial value—in this case, the amount of snow already on the ground at midnight.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Substitution

Formulas

f(x) = 5 + (2/3)x

Theorems

Basic Function Substitution

Suitable Grade Level

Grades 6-8