š(š”)=35(0.92)^š”/5
What is the annual decay rate of the substance? decay rate = __ %
**I am confused I thought that it would either be 92% or 8%**
if t is in years
in one year
.92^0.20 = 0.98
To find the annual decay rate of the substance, we need to determine the percentage by which the substance decays each year.
The given equation is:
š(š”) = 35(0.92)^(š”/5)
In this equation, š” represents the number of years.
To find the annual decay rate, we need to find the value of š· where:
š· = (1 - 0.92) * 100
The decay rate is the complement of the growth rate, which is 1 - growth rate.
Calculating the decay rate:
š· = (1 - 0.92) * 100
š· = 0.08 * 100
š· = 8
Therefore, the annual decay rate of the substance is 8%.
To find the annual decay rate of the substance, we need to understand the formula and how it represents exponential decay.
The given formula is: š(š”)=35(0.92)^(š”/5)
In this formula, 0.92 represents the decay factor. It is less than 1 because it indicates the substance is decaying or decreasing over time.
The exponent š”/5 represents the number of time intervals or periods. Since we are trying to find the annual decay rate, we need to find the decay factor for a one-year interval.
If we substitute š”=1 into the formula, we get:
š(1) = 35(0.92)^(1/5)
Simplifying this expression gives us the value of š(1), which represents the substance's amount after one year.
To find the annual decay rate, we need to compare the amount after one year to the initial amount (35). We can calculate it using the following formula:
Decay rate = ((Initial amount - Amount after one year) / Initial amount) * 100
Now, let's plug in the values:
Amount after one year, š(1) = 35(0.92)^(1/5)
Initial amount = 35
Decay rate = ((35 - š(1)) / 35) * 100
By evaluating this expression, you will find the annual decay rate of the substance in terms of a percentage.