Question

The demand function for a certain commodity is given by p = 100e^-q/2. (p is the price per unit and q is the number of units.)

Answer 1

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 $p=100e^{-q/2}$

(a) Now, we have to find the value of p when q = 6

Substitute q = 6 in the above equation

$p=100e^{-6/2}\\\p=100e^{-3}$

On simplifying, we get

$p=4.97870683679$

Rounding to nearest cents, we have

$p=5.0$

Therefore, the price per units is $5.0

(b)

Now, we have to find q for p = $2.99

$2.99=100e^{-q/2}$

Divide both sides by 100

$0.0299=e^{-q/2}$

Take natural log both sides

$\ln(0.0299)=\ln(e^{-q/2})$

On simplifying, we get

$\ln(0.0299)=-q/2\ln(e)\\\\\ln(0.0299)=-q/2\\\\q=-2\ln \left(0.0299\right)\\\\q=7.0$

Therefore, the number of units demanded = 7