The number of students enrolled at a college is 17,000 and grows 5% each year. Complete parts (a) and (b).
a) Complete the equation y
to find the number of students enrolled after x years.
b) Use your equation to predict the number of students enrolled after years.
After years, there will be
enter your response here students enrolled.
(a) To find the equation y that represents the number of students enrolled after x years, we know that the number of students grows by 5% each year.
We can express the growth rate as a decimal by dividing it by 100: 5% = 5/100 = 0.05.
The formula to calculate the number of students after a certain number of years is:
y = initial number of students * (1 + growth rate)^x
In this case, the initial number of students is 17,000 and the growth rate is 0.05. Plugging these values into the equation, we get:
y = 17,000 * (1 + 0.05)^x
So, the equation to find the number of students enrolled after x years is y = 17,000 * 1.05^x.
(b) To predict the number of students enrolled after a specific number of years, substitute the given value into the equation.
If we are asked to find the number of students enrolled after "years", we replace the "years" in the equation with the specific number of years.
After "years", the equation becomes:
y = 17,000 * 1.05^("years")
Now, to calculate the value, we need the specific number of years.
Please provide the specific number of years so that we can complete the calculation and give you the answer.
a) The equation for finding the number of students enrolled after x years can be represented as:
y = 17,000 * (1 + 0.05)^x
b) To predict the number of students enrolled after a certain number of years, substitute the value of years into the equation:
After **years, there will be **students enrolled.
Please provide the value of "years" so that I can complete the prediction.
a) y = 17000(1.05)^x
b) After 5 years, there will be 20,092.25 students enrolled.