The Clearwater Chemical Company is developing a product that uses enzymes to safely break down the foamy pollution from certain chemical spills. In a test, the company used the new product on foam that initially had a height of 100millimeters. After one hour, the foam had shrunk to a height of 80millimeters.
Let t represent the number of hours since the start of the test. Assuming the foam's height decreased exponentially, which expression best models the foam's height over time?
If the foam's height continued to decrease exponentially, what was the height 5hours after the start of the test?
Round your answer to the nearest whole number.
millimeters
The expression that best models the foam's height over time is: $\text{height} = 100 \cdot e^{-0.223t}$, where $t$ is the number of hours since the start of the test.
To find the height 5 hours after the start of the test, we substitute $t=5$ into the expression: $\text{height} = 100 \cdot e^{-0.223(5)}$. Evaluating this expression, we find that the height 5 hours after the start of the test is approximately 53 millimeters. Rounded to the nearest whole number, the height is 53 millimeters.