Questions: The price of one gallon of unleaded gasoline at the pump reached 1.65 on January 1st of 2004 and continued to rise at the rate of 6 cents per month for the next nine months. Express the price of one gallon of unleaded gasoline as a function of time for the period starting January 2004. What was the price of 18 gallons of gas on May 1st 2004? On September 1st 2004? Let P equal the price per gallon and x equal the number of months since January 2004. Express the price of one gallon of unleaded gasoline as a function of time for the period starting January 2004. P(x)= (Type an expression using x as the variable.)

The price of one gallon of unleaded gasoline at the pump reached 1.65 on January 1st of 2004 and continued to rise at the rate of 6 cents per month for the next nine months. Express the price of one gallon of unleaded gasoline as a function of time for the period starting January 2004. What was the price of 18 gallons of gas on May 1st 2004? On September 1st 2004? Let P equal the price per gallon and x equal the number of months since January 2004. Express the price of one gallon of unleaded gasoline as a function of time for the period starting January 2004. P(x)= (Type an expression using x as the variable.)
Transcript text: The price of one gallon of unleaded gasoline at the pump reached $\$ 1.65$ on January 1st of 2004 and continued to rise at the rate of 6 cents per month for the next nine months. Express the price of one gallon of unleaded gasoline as a function of time for the period starting January 2004. What was the price of 18 gallons of gas on May 1st 2004? On September 1st 2004? Let $P$ equal the price per gallon and $x$ equal the number of months since January 2004. Express the price of one gallon of unleaded gasoline as a function of time for the period starting January 2004. \[ \mathrm{P}(\mathrm{x})=\square \] (Type an expression using $x$ as the variable.)
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Solution

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Express the price of one gallon of unleaded gasoline as a function of time for the period starting January 2004.

Define the variables and initial conditions.

Let \( P(x) \) represent the price per gallon of unleaded gasoline, where \( x \) is the number of months since January 2004. On January 1st, 2004 (\( x = 0 \)), the price is \( \$1.65 \). The price increases at a rate of 6 cents (\( \$0.06 \)) per month.

Formulate the function.

The price \( P(x) \) can be expressed as:
\[ P(x) = 1.65 + 0.06x \]

The price of one gallon of unleaded gasoline as a function of time is:
\[ \boxed{P(x) = 1.65 + 0.06x} \]

What was the price of 18 gallons of gas on May 1st, 2004?

Determine the number of months since January 2004.

May 1st, 2004 is 4 months after January 1st, 2004. Thus, \( x = 4 \).

Calculate the price per gallon on May 1st, 2004.

Using the function \( P(x) = 1.65 + 0.06x \), substitute \( x = 4 \):
\[ P(4) = 1.65 + 0.06(4) = 1.65 + 0.24 = 1.89 \]

Calculate the price of 18 gallons.

The price of 18 gallons is:
\[ 18 \times 1.89 = 34.02 \]

The price of 18 gallons of gas on May 1st, 2004 is:
\[ \boxed{\$34.02} \]

What was the price of 18 gallons of gas on September 1st, 2004?

Determine the number of months since January 2004.

September 1st, 2004 is 8 months after January 1st, 2004. Thus, \( x = 8 \).

Calculate the price per gallon on September 1st, 2004.

Using the function \( P(x) = 1.65 + 0.06x \), substitute \( x = 8 \):
\[ P(8) = 1.65 + 0.06(8) = 1.65 + 0.48 = 2.13 \]

Calculate the price of 18 gallons.

The price of 18 gallons is:
\[ 18 \times 2.13 = 38.34 \]

The price of 18 gallons of gas on September 1st, 2004 is:
\[ \boxed{\$38.34} \]

The price of one gallon of unleaded gasoline as a function of time is:
\[ \boxed{P(x) = 1.65 + 0.06x} \]
The price of 18 gallons of gas on May 1st, 2004 is:
\[ \boxed{\$34.02} \]
The price of 18 gallons of gas on September 1st, 2004 is:
\[ \boxed{\$38.34} \]

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