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Answer:
The initial number of annual births in 2018 is 918,397
The percent decrease in birth rates is 2.37%
The expected number of births in 2021 is 834,379
Step-by-step explanation:
Exponential Decay Function
The exponential function is frequently used to model natural decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
We are given the function that models the annual birth rate for a population of a given country:
[tex]y= 918,397(0.9763)^t[/tex]
Where t represents the number of years since 2018.
a.) We can identify the variables with the actual model by comparing with the general equation, thus: Co=918,397 and 1-r=0.9763.
Solving for r we have r=1-0.9763=0.0237.
This means the initial number of annual births in 2018 (t=0) is 918,397
b.) The percent decrease in birth rates is r=0.0237 = 2.37%
c.) To find the expected number of births in 2021 (t=4 years), we substitute the value of t in the equation of the model:
[tex]y= 918,397(0.9763)^4[/tex]
Calculating:
y = 834,379
The expected number of births in 2021 is 834,379