Scientists Sometimes Use the Formula $f ( t ) = a \sin ( b t + c ) + d$

question 1

Multiple Choice

Scientists sometimes use the formula $f ( t ) = a \sin ( b t + c ) + d$ to simulate temperature variations during the day, with time t in hours, temperature f ( t ) in ${ } ^ { \circ } \mathrm { C }$ , and t=0 corresponding to midnight. Assume that f ( t ) is decreasing at midnight. Determine values of a, b, c, and d that fit the information: the high temperature is 19 ${ } ^ { \circ } \mathrm { C }$ , and the low temperature of -19 ${ } ^ { \circ } \mathrm { C }$ occurs at 4 A.M.

• A) \(a = 19 , b = \frac { \pi } { 24 } , c = - \frac { 5 \pi } { 6 } , d = 0\)
• B) \(a = 25 , b = \frac { \pi } { 12 } , c = - \frac { \pi } { 6 } , d = 25\)
• C) \[a = 38 , b = \frac { \pi } { 6 } , c = - \frac { 5 \pi } { 6 } , d = 0\]
• D) \(a = 19 , b = \frac { \pi } { 24 } , c = - \frac { \pi } { 3 } , d = - 25\)
• E) \(a = 19 , b = \frac { \pi } { 12 } , c = - \frac { 5 \pi } { 6 } , d = 0\)

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Definitions:

Drive Reduction Theory

A motivational theory that argues the primary goal of all behavior is the reduction of drives, which are basic bodily needs.

Motivation

The method that starts, steers, and sustains behaviors aimed at achieving goals.

Reinforcement Value

The degree to which a specific outcome or reward increases the likelihood of a behavior occurring again.

Motivation

The internal drive or process that stimulates an individual to act towards achieving a goal or fulfilling a need.