Answer:
y = 250(0.96^n)
Explanation:
You want an equation for the number of students in the senior class after n years, when it has 250 students now and decreases at 4% per year. You also want to know the number of years until the class is 100 students.
Exponential equation
The exponential equation will have the form ...
y = a·b^x
where 'a' is the initial value, 'b' is the growth factor, and x is the independent variable.
Application
You have an initial value of 250, a growth factor of (1+(-4%)) = 0.96, and an independent variable of 'n', representing the number of years the population has been declining. The equation is ...
y = 250(0.96^n)
100 students
The population will reach 100 students when n has the value that satisfies ...
100 = 250·0.96^n
0.4 = 0.96^n . . . . . . . . . divide by 250
log(0.4) = n·log(0.96) . . . . . take logarithms
n = log(0.4)/log(0.96) ≈ 22.45
The senior class will have about 100 students in 22.45 years.
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Additional comment
The growth factor used in these exponential equations is (1 + growth rate), where the growth rate is the fractional change in the period of interest. The independent variable (x or n) is the number of such periods. Here, the fractional change is given as -4%, a 4% per year decrease. This tells us a period is 1 year. Of course -4% is the decimal fraction -0.04.