a) A growth factor of 1.22 corresponds to a rate of?
b)a growth rate of 6.7% corresponds to a growth factor of?
c)a decay factor pf 0.972 corresponds to a decay rate of?
d)A decay rate of 12.3% corresponds to a decay factor of?
122%
a) To calculate the rate corresponding to a growth factor of 1.22, subtract 1 from the growth factor and multiply the result by 100.
The rate can be calculated as follows:
Rate = (1.22 - 1) * 100
Rate = 0.22 * 100
Rate = 22%
Therefore, a growth factor of 1.22 corresponds to a growth rate of 22%.
b) To calculate the growth factor corresponding to a growth rate of 6.7%, add 1 to the growth rate (in decimal form).
The growth factor can be calculated as follows:
Growth Factor = 1 + 0.067
Growth Factor = 1.067
Therefore, a growth rate of 6.7% corresponds to a growth factor of 1.067.
c) To calculate the decay rate corresponding to a decay factor of 0.972, subtract the decay factor from 1 and multiply the result by 100.
The decay rate can be calculated as follows:
Decay Rate = (1 - 0.972) * 100
Decay Rate = 0.028 * 100
Decay Rate = 2.8%
Therefore, a decay factor of 0.972 corresponds to a decay rate of 2.8%.
d) To calculate the decay factor corresponding to a decay rate of 12.3%, convert the decay rate to decimal form and subtract it from 1.
The decay factor can be calculated as follows:
Decay Factor = 1 - 0.123
Decay Factor = 0.877
Therefore, a decay rate of 12.3% corresponds to a decay factor of 0.877.
To find the corresponding rate or factor, we can use the following formulas:
a) Rate = (Growth Factor - 1) * 100
b) Growth Factor = 1 + (Rate / 100)
c) Decay Rate = (1 - Decay Factor) * 100
d) Decay Factor = 1 - (Decay Rate / 100)
Let's solve each problem using the appropriate formula:
a) To find the rate corresponding to a growth factor of 1.22:
Rate = (1.22 - 1) * 100
= 0.22 * 100
= 22%
Therefore, a growth factor of 1.22 corresponds to a growth rate of 22%.
b) To find the growth factor corresponding to a growth rate of 6.7%:
Growth Factor = 1 + (6.7 / 100)
= 1 + 0.067
= 1.067
Therefore, a growth rate of 6.7% corresponds to a growth factor of 1.067.
c) To find the decay rate corresponding to a decay factor of 0.972:
Decay Rate = (1 - 0.972) * 100
= 0.028 * 100
= 2.8%
Therefore, a decay factor of 0.972 corresponds to a decay rate of 2.8%.
d) To find the decay factor corresponding to a decay rate of 12.3%:
Decay Factor = 1 - (12.3 / 100)
= 1 - 0.123
= 0.877
Therefore, a decay rate of 12.3% corresponds to a decay factor of 0.877.
By using the appropriate formulas, we can find the corresponding rate or factor for different scenarios.