Question

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

Answer 1

Day 0 , A = 150

Day 1 , A = 106.06

Day 2, A = 75

Day 3, A = 53.033

Day 4, A = 37.5

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(1)/(√(2) )`

Substituting the value of lambda in equation 1 we get -

`A = 150 * e^{ln(1)/(√(2) ) ^d}\\A = 150 (1)/(√(2) )^d\\A = 150 (2)^{(-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