Question

PLEASE HELP!!! The amount of polonium-210 remaining, P(t), after t days in a sample can be modeled by the exponential function P(t) = 100e−0.006t, where 100 represents the initial number of grams in the sample. What is an equivalent expression, written as a percentage rate of polonium-210 lost, and how much polonium-210 remains (rounded to the nearest whole number) after 16 days?

Hint: Find the value of e−0.006 on your calculator. (7 points)

P(t) = 100e0.006t, 109 grams remain
P(t) = 100e0.994t, 3 grams remain
P(t) = 100(0.994)t, 91 grams remain
P(t) = 100(0.994)−t, 91 grams remain

Answer 1

`P(t)=100(0.994)^t`

Explanation:

A calculator shows the value of
`e^(-.006) \approx 0.994` meaning that each day, about 99.4% of the sample remains.

The formula
`P(t)=100e^(-0.006t) = 100(e^(-0.006))^t=100(0.994)^t`

Evaluate this at t = 16 to get 91 grams remain.