Math / Algebra

QuestionAt a parking garage in a large city, the charge for parking consists of a flat fee of $\$ 1.00$ plus $\$ 1.50 / \mathrm{hr}$ . (a) Write a linear function to model the cost for parking $P(t)$ for $t$ hours. (b) Evaluate $P(1.7)$ and interpret the meaning in the context of this problem.

Studdy Solution

STEP 1

1. The cost for parking consists of a flat fee of $\$1.00$ plus an additional $\$1.50$ per hour.
2. The function $P(t)$ represents the total cost of parking for $t$ hours.
3. We need to form a linear function that models this cost and evaluate it for a specific value of $t$ .

STEP 2

1. Formulate the linear function $P(t)$ to model the cost of parking.
2. Substitute $t = 1.7$ into the function $P(t)$ and calculate the result.
3. Interpret the meaning of the calculated value $P(1.7)$ in the context of the parking cost.

STEP 3

Formulate the linear function $P(t)$ to model the cost of parking.
The cost consists of a flat fee of $\$1.00$ plus $\$1.50$ per hour. Hence, the linear function can be written as: $P(t) = 1.00 + 1.50t$

STEP 4

Substitute $t = 1.7$ into the function $P(t)$ and calculate the result.
$P(1.7) = 1.00 + 1.50 \times 1.7$

STEP 5

Perform the multiplication and addition to find $P(1.7)$ .
$P(1.7) = 1.00 + 2.55 = 3.55$

STEP 6

Interpret the meaning of the calculated value $P(1.7)$ .
The cost of parking for $1.7$ hours is $\$3.55$ . This means that if someone parks for 1.7 hours at the garage, they will need to pay $\$3.55$ .

Was this helpful?

QuestionAt a parking garage in a large city, the charge for parking consists of a flat fee of $\$ 1.00$ plus $\$ 1.50 / \mathrm{hr}$ . (a) Write a linear function to model the cost for parking $P(t)$ for $t$ hours. (b) Evaluate $P(1.7)$ and interpret the meaning in the context of this problem.

Studdy Solution

STEP 1

1. The cost for parking consists of a flat fee of $\$1.00$ plus an additional $\$1.50$ per hour.
2. The function $P(t)$ represents the total cost of parking for $t$ hours.
3. We need to form a linear function that models this cost and evaluate it for a specific value of $t$ .

STEP 2

1. Formulate the linear function $P(t)$ to model the cost of parking.
2. Substitute $t = 1.7$ into the function $P(t)$ and calculate the result.
3. Interpret the meaning of the calculated value $P(1.7)$ in the context of the parking cost.

STEP 3

Formulate the linear function $P(t)$ to model the cost of parking.
The cost consists of a flat fee of $\$1.00$ plus $\$1.50$ per hour. Hence, the linear function can be written as: $P(t) = 1.00 + 1.50t$

STEP 4

Substitute $t = 1.7$ into the function $P(t)$ and calculate the result.
$P(1.7) = 1.00 + 1.50 \times 1.7$

STEP 5

Perform the multiplication and addition to find $P(1.7)$ .
$P(1.7) = 1.00 + 2.55 = 3.55$

STEP 6

Interpret the meaning of the calculated value $P(1.7)$ .
The cost of parking for $1.7$ hours is $\$3.55$ . This means that if someone parks for 1.7 hours at the garage, they will need to pay $\$3.55$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. The cost for parking consists of a flat fee of $1.00\$1.00$1.00 plus an additional $1.50\$1.50$1.50 per hour.2. The function P(t)P(t)P(t) represents the total cost of parking for ttt hours.3. We need to form a linear function that models this cost and evaluate it for a specific value of ttt.

STEP 2

1. Formulate the linear function P(t)P(t)P(t) to model the cost of parking.2. Substitute t=1.7t = 1.7t=1.7 into the function P(t)P(t)P(t) and calculate the result.3. Interpret the meaning of the calculated value P(1.7)P(1.7)P(1.7) in the context of the parking cost.

STEP 3

Formulate the linear function P(t)P(t)P(t) to model the cost of parking.The cost consists of a flat fee of $1.00\$1.00$1.00 plus $1.50\$1.50$1.50 per hour. Hence, the linear function can be written as: P(t)=1.00+1.50t P(t) = 1.00 + 1.50t P(t)=1.00+1.50t

STEP 4

Substitute t=1.7t = 1.7t=1.7 into the function P(t)P(t)P(t) and calculate the result.P(1.7)=1.00+1.50×1.7 P(1.7) = 1.00 + 1.50 \times 1.7 P(1.7)=1.00+1.50×1.7

STEP 5

Perform the multiplication and addition to find P(1.7)P(1.7)P(1.7).P(1.7)=1.00+2.55=3.55 P(1.7) = 1.00 + 2.55 = 3.55 P(1.7)=1.00+2.55=3.55

STEP 6

Interpret the meaning of the calculated value P(1.7)P(1.7)P(1.7).The cost of parking for 1.71.71.7 hours is $3.55\$3.55$3.55. This means that if someone parks for 1.7 hours at the garage, they will need to pay $3.55\$3.55$3.55.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The cost for parking consists of a flat fee of $\$1.00$ plus an additional $\$1.50$ per hour.
2. The function $P(t)$ represents the total cost of parking for $t$ hours.
3. We need to form a linear function that models this cost and evaluate it for a specific value of $t$ .

1. Formulate the linear function $P(t)$ to model the cost of parking.
2. Substitute $t = 1.7$ into the function $P(t)$ and calculate the result.
3. Interpret the meaning of the calculated value $P(1.7)$ in the context of the parking cost.

Formulate the linear function $P(t)$ to model the cost of parking.
The cost consists of a flat fee of $\$1.00$ plus $\$1.50$ per hour. Hence, the linear function can be written as: $P(t) = 1.00 + 1.50t$

Substitute $t = 1.7$ into the function $P(t)$ and calculate the result.
$P(1.7) = 1.00 + 1.50 \times 1.7$

Perform the multiplication and addition to find $P(1.7)$ .
$P(1.7) = 1.00 + 2.55 = 3.55$

Interpret the meaning of the calculated value $P(1.7)$ .
The cost of parking for $1.7$ hours is $\$3.55$ . This means that if someone parks for 1.7 hours at the garage, they will need to pay $\$3.55$ .