19. Ms. Porter had eight parties at her house last year. The number of guests at each party
2 answers:
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Answer:
Step-by-step explanation:
Let's first find the exponential function that models the situation in year one. The exponential standard form is
where a is the initial value and b is the growth/decay rate in decimal form. If it is growth it is added to 100% of the initial value; if it is decay it is taken away from 100% of the initial value. We are told that the number of cars in year one was 80 million, so
a = 80 (in millions)
If b is increasing by 10%, then we are adding that amount to the initial 100% we started with to give us 100% + 10% = 110% or, in decimal form, 1.1
The model for our situation is
where y is the number of cars after x years goes by. We want to find the difference between years 3 and 2, so we will use our model twice, replacing x with both a 2 and then a 3 and subtracting.
When x = 2:
and
y = 80(1.21) so
y = 96.8 million cars
When x = 3:
and
y = 80(1.331) so
y = 106.48 million cars
The difference between years 3 and 2 is
106.48 - 96.8 = 9.68 million cars
Functions are used to represent graphs, and vice versa.
The function represented by the graph is
The graph (see attachment) is an absolute value graph.
An absolute value graph is represented as:
Where
The vertex is the minimum or the maximum point on the graph.
So, we have:
The function becomes
The function also passes through the point (-1,0).
So, we have:
Remove the absolute bracket
Subtract 3 from both sides
Divide both sides by 3
Substitute -1 for (a) in
Hence, the function represented by the graph is
Read more about absolute value graphs at:
