Poli 761 (a fictitious substance) decays by about 7% every day. How much of a 88 pound sample remains after 9 days?
I thought it would just be A = 88e^(0.07*9), which equals 165.23 pounds, but apparently that's not correct...
You can't always just plug in e for the base of the exponent. After 1 day, .93 remains. After t days, .93^t remains. So, we have
88 * .93^9 = 45.80 lbs
Now, if you want to use e as the base, recall that .93 = e^ln(.93) = e^-.0725
So, .93^t = e^(-.0725t)
In your formula, you have the amount growing, since e^.07 is greater than 1.
ok thanks
To find out how much of the 88-pound sample of Poli 761 remains after 9 days, we can use the formula for exponential decay:
A = P(1 - r)^t
Where:
A is the amount remaining after time t,
P is the initial amount,
r is the decay rate (as a decimal),
and t is the time in days.
In this case, the initial amount P is 88 pounds, the decay rate r is 7% or 0.07, and the time t is 9 days.
Plugging these values into the formula, we get:
A = 88(1 - 0.07)^9
Now let's calculate it step by step:
Step 1: Subtract the decay rate from 1:
1 - 0.07 = 0.93
Step 2: Raise the result to the power of the time:
0.93^9 ≈ 0.478
Step 3: Multiply the result by the initial amount:
88 * 0.478 ≈ 42.024
Therefore, after 9 days, approximately 42.024 pounds of the 88-pound sample of Poli 761 remains.