Question

The temperature of a Tim Hortons Café Mocha over time can be modelled by the following EXPONENTIAL function where T(x) is the temperature in degrees C and x is the elapsed time in minutes. T(x)=20(1/2)^x/30+40
a) What is the parent/base function?
b) What are the values of a, d,k, and c?

Answer 1

a) The parent/base function is y = a(b)^x.

b) In this case, the values of a, b, k, and c are as follows:
- a = 20 (coefficient in front of the exponential function)
- b = 1/2 (base of the exponential function)
- k = 1/30 (coefficient in the exponent, representing the rate at which the temperature decreases over time)
- c = 40 (constant added at the end)