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1 answer:
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Answer:
The slope of f(x) is 1.5
Step-by-step explanation:
step 1
Find the slope of the linear function that has an x-intercept of 2/3 and a y-intercept of -1
so
we have the points
(2/3,0) and (0,-1)
The formula to calculate the slope between two points is equal to
substitute the values
step 2
Find the slope of the function graphed
take the points
(0,-1) and (3,6) approximately
substitute in the formula
step 3
we know that
f(x) represents the function with the smaller slope
The smaller slope is 1.5
therefore
The slope of f(x) is 1.5
Answer:
19 million
Step-by-step explanation:
So generally whenever we express a exponential function, it's in the form:
where a=initial value aka when x=0
in this case, b can be expressed as: , where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213
This gives us the following equation:
To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.
So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.
When x=1, we get: , which can be expressed as a 2.13% increase from year 0
When x=2, we get: , which can be expressed as a 2.13% increase from year 1
when x=3, we get: , which can be expressed as a 2.13% increase from year 2.
In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).
So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990
We get the following equation:
Using a calculator this simplifies to approximately:
Rounding this to the nearest integer would yield 19, and since the values are expressed in millions, the answer would be 19 million