Chapter MPS, Problem 13.10MPS

a.

To determine

State the amplitude, period, and vertical shift of the function.

Answer to Problem 13.10MPS

  $a=4.3,b=0.82year\&k=7.3$

Explanation of Solution

Given information:

An economist indicates that the demand for temporary employment in Sid’s country can be modelled by the function $d=4.3\sin \left(0.82t+0.3\right)+7.3,$ where $t$ is the time in years since January $1995$ .

Calculation:

The general equation is $y=a\sin \left(bt-bh\right)+k,$ here,

  $a=amplitude,b=period,h=phase,shift,andk=vertical,shift.$

Compare the equation $d=4.3\sin \left(0.82t+0.3\right)+7.3,$ with equation $y=a\sin \left(bt-bh\right)+k,$

Hence, the value of $a=\mathrm{4.3.}k=7.3andb=0.82$

Hence, the amplitude, period and the vertical shift is $a=4.3,b=0.82year\&k=7.3$ respectively.

b.

To determine

Interpret the meaning of the function.

Answer to Problem 13.10MPS

Employment will increase from the normal demand and this demand will increase in every $0.82$ year.

Explanation of Solution

Given information:

An economist indicates that the demand for temporary employment in Sid’s country can be modelled by the function $d=4.3\sin \left(0.82t+0.3\right)+7.3,$ where $t$ is the time in years since January $1995$ .

Calculation:

Hence, the amplitude is $4.3$ units, therefore, the difference between the maximum demand and the minimum demand for employment is $4.3$ .

The vertical shift by $7.3$ units implies that the demand for temporary employment will increase from the normal demand and this demand will increase in every $0.82$ year.