How Long Until Superman Regains His Powers?

In summary, Superman will regain his powers in approximately 16.6 days, rounded to the nearest day. This can be calculated using the equation Q(t) = Qe^(rt), where r=-0.138629 and 90% of the kryptonite must decay for Superman to regain his powers.
  • #1
Yohan Lee
2
0

Homework Statement


superman has been disabled by a nearby amount of kryptonite, which decays exponentially. If Superman cannot regain his power until 90% og the kryptonite disintegrates, then how long will it be before he regain his powers?
Use r=-0.138629. Round to the nearest day.
a. 4days c 11days
b 6days d 17days e 21days

Homework Equations


Q(t) = Qe^(rt)

The Attempt at a Solution


i tried 0.9Q=Qe^(-0.138629t)
0.9=e^(-0.138629t)
ln0.9=lne^(-0.138629t)
ln0.9=-0.138629t
ln0.9/-0.138629 =t
t=0.760018
and i was not able to find the answer
 
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  • #2
If 90% has decayed, how much is left?
 
  • #3
Thank you i got 0.1Q=Qe^(-0.138629t)
t= 16.6
 

Related to How Long Until Superman Regains His Powers?

1. What is exponential decay?

Exponential decay is a mathematical concept that describes the decrease in a quantity over time. It is characterized by a constant rate of decay, meaning that the amount being reduced decreases at a consistent percentage over equal intervals of time.

2. How is exponential decay different from exponential growth?

Exponential decay and exponential growth are two sides of the same coin. While exponential decay describes the decrease in a quantity over time, exponential growth describes the increase in a quantity over time. Both follow a similar pattern, but with different rates of change.

3. What is the formula for exponential decay?

The formula for exponential decay is A = A0 * e-kt, where A is the current amount, A0 is the initial amount, k is the decay constant, and t is the time. This formula can be used to calculate the amount of a substance remaining after a certain amount of time.

4. How do I solve exponential decay homework problems?

To solve exponential decay homework problems, you will need to follow the steps of the formula A = A0 * e-kt. You will need to plug in the given values for A0, k, and t, and then use algebraic manipulation to solve for the remaining variable.

5. What are some real-life examples of exponential decay?

Exponential decay can be observed in many natural and man-made processes. Some common examples include radioactive decay, population decline, and the decay of unstable isotopes. Other examples include the half-life of medications and the decrease in value of a car over time.

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