Answer:
<em>C(19)=12 responses</em>
Step-by-step explanation:
<u>Exponential Decay Function</u>
The exponential function is frequently used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function can be expressed as follows:
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The company puts out an advertisement for a job opening. Initially, the company got 90 responses to the advertisement. Each day, the responses declined by 10%.
This is an example where the decay model can be used to calculate the responses to the advertisement at the day t.
The initial value is Co=90, the decaying rate is r=10% = 0.10. The model is written as:
Calculating:
We are required to calculate the number of responses at day t=19, thus:
C(19)=12 responses
Given that
, then
The slope of a tangent line in the polar coordinate is given by:
Thus, we have:
Part A:
For horizontal tangent lines, m = 0.
Thus, we have:
Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:
</span><span>θ = 0
</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488
Part B:
For vertical tangent lines,
Thus, we have:
</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:
</span>θ = <span>4.91718592528713</span>
Answer:
D
Step-by-step explanation:
A squared plus B squared equals C squared