Question

If algae grows at a rate that can be modeled by the exponential function A(t) = ae^rt, what is the surface area of algae on a pond if the initial area of the algae (a) is 2 square meters, the growth rate (r) is 10%, and the algae grows for three days (t)?

Answer 1

Step-by-step explanation

In this problem, we have a model for the growth of algae. The model is described in terms of the function:

`A(t)=a\cdot e^(r\cdot t).`

Where:

• A is the surface area of the algae,

,

• t is the time in days,

,

• a represents the initial area,

,

• r is the growth rate.

From the statement, we know that:

• t = 3 days,

,

• a = 2 m²,

,

• r = 10% = 0.1.

Replacing these data in the formula above, we get:

`A(3)=2m^2\cdot e^(0.1\cdot3)\cong2.7m^2.`Answer

The surface area after 3 days is approximately 2.7 m².