Regents Exam: Algebra I August 2016 (Problem 17 of 37)

The video tutorial explains how to determine which expression best fits the data of a cooling cup of hot chocolate over time. It introduces exponential functions, distinguishing between growth and decay, and analyzes the data to identify it as an exponential decay. The tutorial then evaluates given expressions to find the best fit by testing them with data points, concluding that the first option is correct.

What is the general form of an exponential function?

• f(t) = a * t^r

• f(t) = a * (1 ± r)^t

• f(t) = a / (1 ± r)^t

• f(t) = a + r * t

Which of the following indicates an exponential growth function?

• Base of the exponent is 0.85

• Base of the exponent is 1.15

• Base of the exponent is -0.85

• Base of the exponent is 0.5

What does the initial value 'a' represent in an exponential function?

• The original or initial value

• The rate of growth or decay

• The final value after time t

• The time variable

Which base value indicates an exponential decay function?

• 1.15

• 0.85

• 2.0

• 1.5

How can you verify which expression best fits the data?

• By analyzing the final value

• By comparing the rate of growth

• By substituting a data point and checking for a true statement

• By checking if the initial value matches