The function f(x)=501170〖(0.98)〗^x gives the population of a Texas city x years after 1995.
1 answer:
Answer:
The population in 1995
501170
Is the population increasing or decreasing?
The population is decreasing
The rate of population change
population in the year 2020
302439
Step-by-step explanation:
Since 1995 is the base year, the population in 1995 is simply found by setting x equal to 0 in the given function;
The population is clearly decreasing over time since the base of the exponent, 0.98, is less than 1.
The rate of population change is obtained by differentiating the function with respect to x using the rule;
The population in the year 2020 is obtained by setting x equal to 25 in the population function since 2020-1995 = 25;
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The functions are illustrations of function transformations
The transformation from f(x) to g(x) is reflecting across the y-axis, and then shifting 2 units up
<h3>How to determine the transformations</h3>The equation of the function is given as:
The parent function of the above equation is:
First, the function f(x) is reflected across the y-axis to give
Next, the function is shifted 2 units up.
So, we have:
Rewrite as:
Express f(-x) + 2 as g(x).
So, we have:
Hence, the transformation from f(x) to g(x) is reflecting across the y-axis, and then shifting 2 units up
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