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Answer:
<em>The initial number of annual births in 2018 is 918,397</em>
<em>The percent decrease in birth rates is 2.37%</em>
<em>The expected number of births in 2021 is 834,379</em>
Step-by-step explanation:
<u>Exponential Decay Function</u>
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:
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:
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:
Calculating:
y = 834,379
The expected number of births in 2021 is 834,379
Answer:
Part a)
Part b)
Step-by-step explanation:
see the attached figure with letters to better understand the problem
Part a) Find the length AB
Applying the Pythagoras Theorem in the right triangle ABH
where
AB is the hypotenuse (the greater side)
AH and HB are the legs of the right triangle
we have
substitute the values
Part a) Find the length AC
Applying the Pythagoras Theorem in the right triangle ABC
where
AC is the hypotenuse (the greater side)
AB and BC are the legs of the right triangle
we have
substitute
