Math / Algebra

QuestionALEKS - 2024 Fall - College Alga A ALEKS-Alden Scott-Knowled www-awa.aleks.com/alekscgi//x/lsl.exe/10_u-lgNsIkr7j8P3jH-IQgKSJS_J3Lykq19bMqn3Sx1kuBwVjDD2XFImfpifl. C. K12 Bookmarks 品 Mall - Scott, Aiden E. Sioux Falls SD 49-5 e-hallpass Dashboard Knowledge C Question 3 Aiden
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 34 Españot minutes of calls is $\$ 25.24$ , and the remaining credit after 58 minutes of calls is $\$ 21.88$ . What is the remaining credit after 76 minutes of calls? s! $\square$ $\times$ 5 IDon't Know SNopmit

Studdy Solution

STEP 1

1. The credit remaining on a phone card is a linear function of the total calling time.
2. After 34 minutes, the remaining credit is \$25.24.
3. After 58 minutes, the remaining credit is \$21.88.
4. We need to find the remaining credit after 76 minutes.

STEP 2

1. Identify the linear function form.
2. Calculate the slope of the linear function.
3. Determine the equation of the line.
4. Use the equation to find the remaining credit after 76 minutes.

STEP 3

Identify the linear function form. The linear function can be expressed as:
$C(t) = mt + b$
where $C(t)$ is the remaining credit, $t$ is the total calling time, $m$ is the slope, and $b$ is the y-intercept.

STEP 4

Calculate the slope of the linear function using the two given points: $(34, 25.24)$ and $(58, 21.88)$ .
The slope $m$ is calculated as:
$m = \frac{21.88 - 25.24}{58 - 34}$
$m = \frac{-3.36}{24}$
$m = -0.14$

STEP 5

Determine the equation of the line using the slope and one of the points, say $(34, 25.24)$ .
Using the point-slope form:
$C(t) - 25.24 = -0.14(t - 34)$
Simplify to find the y-intercept $b$ :
$C(t) = -0.14t + 25.24 + 0.14 \times 34$
$C(t) = -0.14t + 25.24 + 4.76$
$C(t) = -0.14t + 30$

STEP 6

Use the equation to find the remaining credit after 76 minutes:
$C(76) = -0.14 \times 76 + 30$
$C(76) = -10.64 + 30$
$C(76) = 19.36$
The remaining credit after 76 minutes is:
$\boxed{19.36}$

Was this helpful?

Studdy Solution

STEP 1

1. The credit remaining on a phone card is a linear function of the total calling time.
2. After 34 minutes, the remaining credit is \$25.24.
3. After 58 minutes, the remaining credit is \$21.88.
4. We need to find the remaining credit after 76 minutes.

STEP 2

1. Identify the linear function form.
2. Calculate the slope of the linear function.
3. Determine the equation of the line.
4. Use the equation to find the remaining credit after 76 minutes.

STEP 3

Identify the linear function form. The linear function can be expressed as:
$C(t) = mt + b$
where $C(t)$ is the remaining credit, $t$ is the total calling time, $m$ is the slope, and $b$ is the y-intercept.

STEP 4

Calculate the slope of the linear function using the two given points: $(34, 25.24)$ and $(58, 21.88)$ .
The slope $m$ is calculated as:
$m = \frac{21.88 - 25.24}{58 - 34}$
$m = \frac{-3.36}{24}$
$m = -0.14$

STEP 5

Determine the equation of the line using the slope and one of the points, say $(34, 25.24)$ .
Using the point-slope form:
$C(t) - 25.24 = -0.14(t - 34)$
Simplify to find the y-intercept $b$ :
$C(t) = -0.14t + 25.24 + 0.14 \times 34$
$C(t) = -0.14t + 25.24 + 4.76$
$C(t) = -0.14t + 30$

STEP 6

Use the equation to find the remaining credit after 76 minutes:
$C(76) = -0.14 \times 76 + 30$
$C(76) = -10.64 + 30$
$C(76) = 19.36$
The remaining credit after 76 minutes is:
$\boxed{19.36}$

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 credit remaining on a phone card is a linear function of the total calling time.2. After 34 minutes, the remaining credit is \$25.24.3. After 58 minutes, the remaining credit is \$21.88.4. We need to find the remaining credit after 76 minutes.

STEP 2

1. Identify the linear function form.2. Calculate the slope of the linear function.3. Determine the equation of the line.4. Use the equation to find the remaining credit after 76 minutes.

STEP 3

Identify the linear function form. The linear function can be expressed as:C(t)=mt+b C(t) = mt + b C(t)=mt+bwhere C(t) C(t) C(t) is the remaining credit, t t t is the total calling time, m m m is the slope, and b b b is the y-intercept.

STEP 4

STEP 5

STEP 6

Use the equation to find the remaining credit after 76 minutes:C(76)=−0.14×76+30 C(76) = -0.14 \times 76 + 30 C(76)=−0.14×76+30C(76)=−10.64+30 C(76) = -10.64 + 30 C(76)=−10.64+30C(76)=19.36 C(76) = 19.36 C(76)=19.36The remaining credit after 76 minutes is:19.36 \boxed{19.36} 19.36​

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 credit remaining on a phone card is a linear function of the total calling time.
2. After 34 minutes, the remaining credit is \$25.24.
3. After 58 minutes, the remaining credit is \$21.88.
4. We need to find the remaining credit after 76 minutes.

1. Identify the linear function form.
2. Calculate the slope of the linear function.
3. Determine the equation of the line.
4. Use the equation to find the remaining credit after 76 minutes.

Identify the linear function form. The linear function can be expressed as:
$C(t) = mt + b$
where $C(t)$ is the remaining credit, $t$ is the total calling time, $m$ is the slope, and $b$ is the y-intercept.

Use the equation to find the remaining credit after 76 minutes:
$C(76) = -0.14 \times 76 + 30$
$C(76) = -10.64 + 30$
$C(76) = 19.36$
The remaining credit after 76 minutes is:
$\boxed{19.36}$