what is the decay rate:
initial amount: 6
decay factor: 0.98
decay factor: ?
decay rate = 1 - decay factor
....
To find the decay rate, we need to know the formula for exponential decay and the values of the initial amount and decay factor. The formula for exponential decay is:
N = N0 * (decay factor)^t
Where:
N = final amount
N0 = initial amount
decay factor = the rate at which the initial amount decreases over time
t = time
From the given information, the initial amount is 6 and the decay factor is 0.98. Now we can substitute these values into the formula:
N = 6 * (0.98)^t
Since we are looking for the decay factor, we need to solve for (0.98)^t. Taking the natural logarithm (ln) of both sides of the equation will help us isolate the exponent:
ln(N) = ln(6 * (0.98)^t)
ln(N) = ln(6) + ln(0.98^t)
Now we can simplify the equation:
ln(N) = ln(6) + t * ln(0.98)
To find the decay factor (0.98) from this equation, we need to solve for t using logarithmic methods. However, without the value of N or the specific time t, we cannot determine the exact decay factor. We need more information to proceed with the calculation.
To find the decay rate, you would use the formula:
decay factor = decay rate / initial amount
Given that the initial amount is 6 and the decay factor is 0.98, we can rearrange the formula to solve for the decay rate:
decay rate = decay factor * initial amount
Plugging in the values, we have:
decay rate = 0.98 * 6
Simplifying the calculation:
decay rate = 5.88