Question

a small town has two local high schools. high school a currently has 400 students and is projected to grow by 25 students each year. high school b currently has 250 students and is projected to grow by 50 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 2 years. y click twice to plot each line. click a line to delete it. 1000 950 900 850 800 750 700 650 600 550 500 450 400 350 300

Explanation:

Step1: Define the functions for A and B

For High School A, the initial number of students is 400 and it grows by 25 each year. So the function is \( A(t)=400 + 25t \). For High School B, the initial number is 250 and it grows by 50 each year, so \( B(t)=250+50t \).

Step2: Calculate A(2)

Substitute \( t = 2 \) into \( A(t) \): \( A(2)=400+25\times2=400 + 50 = 450 \).

Step3: Calculate B(2)

Substitute \( t = 2 \) into \( B(t) \): \( B(2)=250+50\times2=250 + 100 = 350 \). Wait, no, wait, 250 + 100 is 350? Wait, no, 250+502=250 + 100=350? Wait, no, that can't be. Wait, no, 400 +252=450, 250+502=350? Wait, no, that would mean A has more. Wait, but let's recalculate. 252=50, 400+50=450. 502=100, 250+100=350. Wait, but that seems A has more. Wait, but maybe I made a mistake. Wait, no, the problem says High School A has 400, grows by 25, High School B has 250, grows by 50. So after 2 years, A: 400 +252=450, B:250 +502=350. So A has more. Wait, but let me check again. 252=50, 400+50=450. 50*2=100, 250+100=350. Yes, so A(2)=450, B(2)=350. So High School A has more students in 2 years. Wait, but maybe I messed up the functions. Wait, the growth rate: A grows by 25 per year, B by 50. But initial A is 400, B is 250. So after t years, A: 400 +25t, B:250 +50t. So at t=2, A: 400+50=450, B:250+100=350. So A is 450, B is 350. So A has more.

Answer:

High School A