Question Bank / Math / Nonlinear Functions
Nonlinear functions SAT question
Math · Advanced Math · Hard · Answer it here, explanation included.
Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70 degrees Fahrenheit (°F). The temperature of the hot chocolate was 185°F at 6:00 p.m. when it started cooling. The temperature of the hot chocolate was 156°F at 6:05 p.m. and 135°F at 6:10 p.m. The hot chocolate’s temperature continued to decrease. Of the following functions, which best models the temperature 
, in degrees Fahrenheit, of Kao’s hot chocolate m minutes after it started cooling?
ExplanationShow
Choice D is correct. The hot chocolate cools from 185°F over time, never going lower than the room temperature, 70°F. Since the base of the exponent in this function, 0.75, is less than 1, 
decreases as time increases. Using the function, the temperature, in °F, at 6:00 p.m. can be estimated as 
and is equal to 
. The temperature, in °F, at 6:05 p.m. can be estimated as 
and is equal to 
, which is approximately 156°F. Finally, the temperature, in °F, at 6:10 p.m. can be estimated as 
and is equal to 
, which is approximately 135°F. Since these three given values of m and their corresponding values for can be verified using the function 
, this is the best function out of the given choices to model the temperature of Kao’s hot chocolate after m minutes.
Choice A is incorrect because the base of the exponent,
, results in the value of increasing over time rather than decreasing. Choice B is incorrect because when m is large enough, becomes less than 70. Choice C is incorrect because the maximum value of at 6:00 p.m. is 115°F, not 185°F.
Drill this skill on Aceit
Adaptive practice, a daily plan, and score tracking take a free account so we can save your work.
More Nonlinear functions questions
- A rectangle has a length that is 15 times its width. The function y=15ww represents this situation, where y is the area, in square feet, of the rectangle and y>0. Which of the fo
- The quadratic function h is defined as shown. In the xy-plane, the graph of intersects the x-axis at the points and , where t is a constant. What is the value of t ?
- The function f is defined by f(x)=(-8)(2)x+22. What is the y-intercept of the graph of y=f(x) in the xy-plane?
- All values are approximate. The parabola opens downward. The vertex of the parabola is at (0.6 comma 5.5). The parabola passes through the following points: (0.0 comma 3.8) (0.6 c
- fx=9,0000.66x The given function f models the number of advertisements a company sent to its clients each year, where x represents the number of years since 1997, and 0≤x≤5. If
- The first term of a sequence is 9 . Each term after the first is 4 times the preceding term. If w represents the n th term of the sequence, which equation gives w in terms of n