The a) Initial amount a is 13000.
b) Growth factor b is 1.06.
c) After one year, students = 13000 * 1.06.
d) Equation: y = 13000 * 1.06.
e) After 21 years, predict students ≈ 30816.
a) The initial amount, denoted as "a," is 13,000 students.
b) The percent rate of change, or growth factor, denoted as "b," is calculated by adding 1 to the percentage change, resulting in 1 + 0.06 = 1.06.
c) To determine the number of students enrolled after one year, you multiply the initial amount by the growth factor: 13,000 * 1.06 = 13,780 students.
d) The equation to represent the number of students, "y," after x years is given by y = 13000⋅1.06^x .
e) Using the equation, we can predict the number of students enrolled after 21 years by substituting x with 21:
y=13000⋅1.06^21.
Calculating this yields approximately 30,967 students.
Therefore, after 21 years, there will be approximately 30,967 students enrolled at the college.
Rounded to the nearest whole number, this prediction suggests that there will be 30,967 students.
It's essential to note that this prediction assumes the growth rate remains constant at 6% each year.
Factors such as changes in enrollment policies, external events, or economic conditions could affect the actual number of students in the future.
Question
The number of students enrolled at a college is 13,000 and grows 6% each year. Complete parts (a) through (e). a) The initial amount a is 13000. b) The percent rate of change is 6%, so the growth factor b is 1+0.06=1.06. c) To find the number of students enrolled after one year, you calculate 13.000· 1.06. d) Complete the equation y=13000· 1.06 to find the number of students enrolled after x years. e) Use your equation to predict the number of students enrolled after 21 years. After 21 years, there will be □ students enrolled. (Round to the nearest whole number as needed.)