Math / Algebra

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A small town has two local high schools. High School A currently has 300 students and is projected to grow by 50 students each year. High School B currently has 450 students and is projected to grow by 25 students each year. Let $A$ represent the number of students in High School $A$ in $t$ years, and let $B$ represent the number of students in High School B after $t$ years. Graph each function and determine which high school is projected to have more students in 8 years.

Studdy Solution

STEP 1

1. High School A starts with 300 students and grows by 50 students each year.
2. High School B starts with 450 students and grows by 25 students each year.
3. We need to determine the number of students in each high school after 8 years.

STEP 2

1. Create expressions for the number of students in each high school as functions of time.
2. Evaluate these expressions at $t = 8$ years.
3. Compare the results to determine which high school has more students.

STEP 3

Create the expression for High School A.
The number of students in High School A after $t$ years is given by: $A(t) = 300 + 50t$

STEP 4

Create the expression for High School B.
The number of students in High School B after $t$ years is given by: $B(t) = 450 + 25t$

STEP 5

Evaluate $A(t)$ at $t = 8$ .
$A(8) = 300 + 50 \times 8 = 300 + 400 = 700$

STEP 6

Evaluate $B(t)$ at $t = 8$ .
$B(8) = 450 + 25 \times 8 = 450 + 200 = 650$

STEP 7

Compare $A(8)$ and $B(8)$ .
Since $A(8) = 700$ and $B(8) = 650$ , High School A is projected to have more students in 8 years.
The high school projected to have more students in 8 years is:
$\text{High School A}$

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Studdy Solution

STEP 1

1. High School A starts with 300 students and grows by 50 students each year.
2. High School B starts with 450 students and grows by 25 students each year.
3. We need to determine the number of students in each high school after 8 years.

STEP 2

1. Create expressions for the number of students in each high school as functions of time.
2. Evaluate these expressions at $t = 8$ years.
3. Compare the results to determine which high school has more students.

STEP 3

Create the expression for High School A.
The number of students in High School A after $t$ years is given by: $A(t) = 300 + 50t$

STEP 4

Create the expression for High School B.
The number of students in High School B after $t$ years is given by: $B(t) = 450 + 25t$

STEP 5

Evaluate $A(t)$ at $t = 8$ .
$A(8) = 300 + 50 \times 8 = 300 + 400 = 700$

STEP 6

Evaluate $B(t)$ at $t = 8$ .
$B(8) = 450 + 25 \times 8 = 450 + 200 = 650$

STEP 7

Compare $A(8)$ and $B(8)$ .
Since $A(8) = 700$ and $B(8) = 650$ , High School A is projected to have more students in 8 years.
The high school projected to have more students in 8 years is:
$\text{High School A}$

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Studdy Solution

STEP 1

1. High School A starts with 300 students and grows by 50 students each year.2. High School B starts with 450 students and grows by 25 students each year.3. We need to determine the number of students in each high school after 8 years.

STEP 2

1. Create expressions for the number of students in each high school as functions of time.2. Evaluate these expressions at t=8 t = 8 t=8 years.3. Compare the results to determine which high school has more students.

STEP 3

Create the expression for High School A. The number of students in High School A after t t t years is given by: A(t)=300+50t A(t) = 300 + 50t A(t)=300+50t

STEP 4

Create the expression for High School B.The number of students in High School B after t t t years is given by: B(t)=450+25t B(t) = 450 + 25t B(t)=450+25t

STEP 5

Evaluate A(t) A(t) A(t) at t=8 t = 8 t=8.A(8)=300+50×8=300+400=700 A(8) = 300 + 50 \times 8 = 300 + 400 = 700 A(8)=300+50×8=300+400=700

STEP 6

Evaluate B(t) B(t) B(t) at t=8 t = 8 t=8.B(8)=450+25×8=450+200=650 B(8) = 450 + 25 \times 8 = 450 + 200 = 650 B(8)=450+25×8=450+200=650

STEP 7

Compare A(8) A(8) A(8) and B(8) B(8) B(8).Since A(8)=700 A(8) = 700 A(8)=700 and B(8)=650 B(8) = 650 B(8)=650, High School A is projected to have more students in 8 years. The high school projected to have more students in 8 years is:High School A \text{High School A} High School A

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1. High School A starts with 300 students and grows by 50 students each year.
2. High School B starts with 450 students and grows by 25 students each year.
3. We need to determine the number of students in each high school after 8 years.

1. Create expressions for the number of students in each high school as functions of time.
2. Evaluate these expressions at $t = 8$ years.
3. Compare the results to determine which high school has more students.

Create the expression for High School A.
The number of students in High School A after $t$ years is given by: $A(t) = 300 + 50t$

Create the expression for High School B.
The number of students in High School B after $t$ years is given by: $B(t) = 450 + 25t$

Evaluate $A(t)$ at $t = 8$ .
$A(8) = 300 + 50 \times 8 = 300 + 400 = 700$

Evaluate $B(t)$ at $t = 8$ .
$B(8) = 450 + 25 \times 8 = 450 + 200 = 650$

Compare $A(8)$ and $B(8)$ .
Since $A(8) = 700$ and $B(8) = 650$ , High School A is projected to have more students in 8 years.
The high school projected to have more students in 8 years is:
$\text{High School A}$