Question

Given the following equation: y = cnat², where n is an integer with no units, c is a number between zero and one with no units, the variable t has units of seconds and y is expressed in meters, determine which of the following statements is true?

1) The value of y increases as the value of n increases.
2) The value of y decreases as the value of c increases.
3) The value of y increases as the value of t increases.
4) The value of y is always equal to zero.

Answer 1

The value of y increases as n and t increase; y is not necessarily zero, and y does not decrease with an increase in c.

Step-by-step explanation:

The equation given is y = cnat², where n is an integer, c is a number between zero and one, and t has units of seconds with y expressed in meters. Analyzing the relationship between the variables, we can determine the correct statements:

• The value of y increases as the value of n increases since n is an exponent applied to variable t which is squared; this will make y larger for larger n.
• The value of y decreases as the value of c increases is false because c is a scaling factor that will directly increase the value of y when c increases, provided it remains between zero and one.
• The value of y increases as the value of t increases since t is squared in the equation, any increase in t would result in a quadratic increase in y.
• The statement that value of y is always equal to zero is false as y's value depends on the values of c, n, and t.

Therefore, the correct statements from the options provided are: 1) The value of y increases as the value of n increases, and 3) The value of y increases as the value of t increases.