Question

The area, in square meters, of a pond covers by an algae bloom decreases exponentially after a treatment is applied

Answer 1

Answer:

Day 0 , A = 150

Day 1 , A = 106.06

Day 2, A = 75

Day 3, A = 53.033

Day 4, A = 37.5

Step-by-step explanation:

The complete question is attached below

The exponential decay for area is depicted by

$A = A_0 * e^{\lambda*d}$ ------Eq (1)

Substituting the values given in the attachment, we get -

$75 = 150 * e^{\lambda*2}$

On solving for lambda we get -

$\lambda = ln\frac{1}{\sqrt{2} }$

Substituting the value of lambda in equation 1 we get -

$A = 150 * e^{ln\frac{1}{\sqrt{2} } ^d}\\A = 150 \frac{1}{\sqrt{2} }^d\\A = 150 (2)^{\frac{-d}{2}$

Substituting the value of d one by one we get

Day 0 , A = 150

Day 1 , A = 106.06

Day 2, A = 75

Day 3, A = 53.033

Day 4, A = 37.5