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pt math - Savec PT1 in GENMATH (By pair) 1. Formulate a r...

Aug 28, 2024

Solution by Steps

step 1

Let's formulate a real-life word problem involving a function. Suppose a car travels at a speed of 60 km/h. We want to find the distance traveled after a certain time

t

in hours. The function can be expressed as

d(t) = 60t

, where

d

is the distance in kilometers

step 2

To solve the problem, we can find the distance traveled after 2 hours. We substitute

t = 2

into the function:

d(2) = 60 \times 2

step 3

Calculating the distance:

d(2) = 120

km. Therefore, the car travels 120 kilometers in 2 hours

step 4

The solution is complete, and we can write it down on bond paper as required

Answer

The car travels 120 kilometers in 2 hours.

Key Concept

A function relates inputs to outputs, allowing us to model real-life situations.

Explanation

In this case, the function

d(t) = 60t

helps us determine the distance based on time, illustrating how functions can be applied in practical scenarios.

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Solution by Steps

step 1

Now, let's formulate a real-life word problem involving a rational function. Suppose a company produces

x

units of a product, and the cost

C(x)

to produce

x

units is given by the rational function

C(x) = \frac{1000}{x} + 50

. We want to find the cost of producing 10 units

step 2

To solve the problem, we substitute

x = 10

into the cost function:

C(10) = \frac{1000}{10} + 50

step 3

Calculating the cost:

C(10) = 100 + 50 = 150

. Therefore, the cost of producing 10 units is 150 currency units

step 4

The solution is complete, and we can write it down on bond paper as required

Answer

The cost of producing 10 units is 150 currency units.

Key Concept

A rational function is a ratio of two polynomials, often used to model real-life situations involving rates or costs.

Explanation

In this case, the rational function

C(x) = \frac{1000}{x} + 50

allows us to calculate the cost based on the number of units produced, demonstrating the application of rational functions in economics.