Question

the number of students enrolled at a college is 16,000 and grows 4% each year. complete parts (a) through (e)
a) the initial amount a is 16,000.
b) the percent rate of change is 4%, so the growth factor b is 1 + 0.04 = 1.04
c) to find the number of students enrolled after one year, you calculate 16,000·1.04
d) complete the equation $y = 16000·1.04^x$ to find the number of students enrolled after x years.
e) use your equation to predict the number of students enrolled after 26 years.
after 26 years, there will be \\(\square\\) students enrolled.
(round to the nearest whole number as needed.)

Explanation:

Step1: Identify the formula

We use the exponential growth formula \( y = a \cdot b^x \), where \( a = 16000 \), \( b = 1.04 \), and \( x = 26 \).

Step2: Substitute the values

Substitute \( a = 16000 \), \( b = 1.04 \), and \( x = 26 \) into the formula: \( y = 16000 \cdot (1.04)^{26} \)

Step3: Calculate \( (1.04)^{26} \)

Using a calculator, \( (1.04)^{26}\approx2.772464 \)

Step4: Multiply by the initial amount

Multiply 16000 by 2.772464: \( 16000\times2.772464 = 44359.424 \)

Step5: Round to the nearest whole number

Rounding 44359.424 to the nearest whole number gives 44359.

Answer:

44359