I don't understand the topic we're learning in math. /:
Provide an explanation, steps on how you figured the answer out, and of course, the answer.
Tell whether the abe represents an exponential function. If so, write a rule for the function.
x: -2, -1, 0, 1, 2
y: 25, 5, 1, 1/5, 1/25
To determine if a set of data represents an exponential function, you need to check whether the ratios of y-values (dependent variable) and x-values (independent variable) remain constant.
Looking at the given set of data:
x: -2, -1, 0, 1, 2
y: 25, 5, 1, 1/5, 1/25
Let's calculate the ratios of consecutive y-values:
Ratio between 25 and 5: 25/5 = 5
Ratio between 5 and 1: 5/1 = 5
Ratio between 1 and 1/5: 1/(1/5) = 5
Ratio between 1/5 and 1/25: (1/5)/(1/25) = 5
Since the ratio of consecutive y-values remains constant at 5, we can conclude that the given set of data represents an exponential function.
To write the rule for the function, we can observe that each y-value is obtained by raising 1/5 to the power of the corresponding x-value. Therefore, the rule for the exponential function is:
f(x) = (1/5)^x
The answer is that the given set of data represents an exponential function, and the rule for the function is f(x) = (1/5)^x.