How do you use the exponential decay formula?

Answer 1

I'll use an example from radioactive decay:

#N_t=N_0e^(-lambdat)#
#N_t# = number of undecayed atoms after time #t#
#N_0# = initial number of atoms
#lambda# = decay constant.
#t# = time elapsed.
" #I^131# is a radioactive isotope with a half - life of 8 days. Starting with a mass of 5g, what mass will remain after 10 days? "
#t_((1)/(2)) =0.693/lambda#
So #lambda=0.693/t_((1)/(2)) =0.693/8 = 0.0866d^(-1)#

Taking natural logs of the decay equation we get:

#lnN_t=lnN_0-lambdat#
So #lnN_t=ln(5) - 0.0866xx10#
#lnN_t = 1.61-0.866=0.744#
From which #N_t =2.1g#

I can use grams instead of number of atoms as they are proportional so the constant will cancel out.

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Answer 2

To use the exponential decay formula, which describes the decrease in value of a quantity over time, follow these steps:

  1. Identify the initial value of the quantity (denoted as ( P_0 )).
  2. Determine the rate of decay (denoted as ( r )) as a decimal or fraction.
  3. Find the time elapsed (denoted as ( t )) since the initial measurement.
  4. Use the exponential decay formula: ( P(t) = P_0 \times e^{-rt} ), where ( e ) is Euler's number (( \approx 2.71828 )).

Substitute the values of ( P_0 ), ( r ), and ( t ) into the formula and calculate ( P(t) ), which represents the quantity's value at time ( t ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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