Answer:
(a) the price per units is $5.0
(b)the number of units demanded = 7
Step-by-step explanation:
The demand function is given by [tex]p=100e^{-q/2}[/tex]
(a) Now, we have to find the value of p when q = 6
Substitute q = 6 in the above equation
[tex]p=100e^{-6/2}\\\p=100e^{-3}[/tex]
On simplifying, we get
[tex]p=4.97870683679[/tex]
Rounding to nearest cents, we have
[tex]p=5.0[/tex]
Therefore, the price per units is $5.0
(b)
Now, we have to find q for p = $2.99
[tex]2.99=100e^{-q/2}[/tex]
Divide both sides by 100
[tex]0.0299=e^{-q/2}[/tex]
Take natural log both sides
[tex]\ln(0.0299)=\ln(e^{-q/2})[/tex]
On simplifying, we get
[tex]\ln(0.0299)=-q/2\ln(e)\\\\\ln(0.0299)=-q/2\\\\q=-2\ln \left(0.0299\right)\\\\q=7.0[/tex]
Therefore, the number of units demanded = 7
