There was a sample of
550
milligrams of a radioactive substance to start a study. Since then, the sample has decayed by
5.2%
each year.
Let
t
be the number of years since the start of the study. Let
y
be the mass of the sample in milligrams.
Write an exponential function showing the relationship between
y
and
t
.
To write an exponential function representing the relationship between y (mass of the radioactive substance) and t (number of years since the start of the study), we can use the general exponential decay formula:
y = y0 * (1 - r)^t
Where:
- y0 is the initial mass of the sample at the start of the study (550 milligrams in this case)
- r is the decay rate per year (5.2% or 0.052 in decimal form)
Substituting these values into the exponential decay formula, the equation becomes:
y = 550 * (1 - 0.052)^t
To write an exponential function showing the relationship between y and t, we need to consider the decay factor and the initial amount of the substance.
Given that the sample has decayed by 5.2% each year, the decay factor can be calculated as 1 minus the decay percentage, which is 1 - 0.052 = 0.948.
Since we're starting with a sample of 550 milligrams, the exponential function can be written as:
y = 550 * 0.948^t
In this function, t represents the number of years since the start of the study, and y represents the mass of the sample in milligrams.