Question

The water level of a lake started at 60 feet. During a drought the water level dropped 6% each week. Write an exponential function that describes the water level in terms of the number of weeks.
Weeks: 0, 1, 2, 3, 4.
Water Level: 60, 56.4, 53.02, 49.84, 46.84.
Points on graph: 60, 56.4, 53.02, 49.84, 46.84.
y=_____

Answer 1

To write an exponential function that describes the water level of the lake in terms of the number of weeks, we can use the general form of an exponential decay function:

\[
y = a(1 - r)^t
\]

Where:
- \( y \) is the water level after \( t \) weeks,
- \( a \) is the initial amount (the water level at week 0),
- \( r \) is the rate of decay (as a decimal),
- \( t \) is the time in weeks.

In this case:
- The initial water level \( a = 60 \) feet,
- The decay rate \( r = 0.06 \) (since the water level drops by 6%).

Thus, the function becomes:

\[
y = 60(1 - 0.06)^t
\]

Simplifying this, we get:

\[
y = 60(0.94)^t
\]

So, the exponential function that describes the water level in terms of the number of weeks \( t \) is:

\[
y = 60(0.94)^t
\]