Question

An environmental group is tracking a fast-growing algae's coverage on a nearby pond. When

the group first measured the algae, it covered 3 square meters of the pond. They expect the
area of the pond covered by algae will double each day.
Write an exponential equation in the form = a(b)^x that can model the area of the pond
covered by algae, y, in x days.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =

How much of the pond is expected to be covered by algae after 4 days?

Answer 1

• y = 3(2^x)
• 48 m² after 4 days

Explanation:

You want an exponential function of the form y = a(b^x) that models algae growth that initially covers 3 square meters of a pond and doubles in area each day.

Exponential function

The function y = a(b^x) has an initial value of 'a', which the problem statement tells us is 3 (square meters). The value 'b' is the growth factor, which the problem statement tells us is 2 each day.

The desired exponential equation is ...

y = 3(2^x)

4 days

When x=4, the function evaluates to ...

y = 3(2^4) = 3(16) = 48 . . . . square meters

After 4 days, 48 square meters of the pond is expected to be covered by algae.

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