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2 answers:
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Answer:
C. When the survey was initially conducted average sales of smartphones was 1.7 millions units.
Step-by-step explanation:
We have been given that the average annual sales of smartphones, in million units, n years after the survey is conducted is modeled by function , where the parameter b is an unknown positive base.
We are asked to find the true statement about our given function.
A. If b= 1.45, the annual growth rate of the sales of smartphones is 145%.
Since we know that b equals (1+r) for growth function, where r is in decimal form.
If b=1.45, it means that the annual growth rate will be 45% as 0.45 is decimal form of 45%, therefore, statement A is not true.
B. If b= 1.02, annual sales of smartphones will double in 2 years.
If b=1.02, it means that the annual growth rate will be 2% as 0.02 is decimal form of 2%, therefore, statement B is not true.
C. When the survey was initially conducted average sales of smartphones was 1.7 millions units.
Since we know that an exponential function is in form , where a in initial value of function. We can see from our given function that a equals 1.7, therefore option C is a true statement.
D. The average sales of smartphones increases by 1.7 millions units every year.
Since our function is not a linear function, instead it is an exponential function, so rate of change can not be constant.
Therefore, option D is not true regarding our given function.
Step-by-step explanation:
The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as
.
This definition of the absolute function can be explained geometrically to be similar to the straight line , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line
where
(shown as the orange dotted line), the segment of the line is reflected across the <em>x</em>-axis.
First, we simplify the expression.
.
We, now, can simply visualise the straight line, , as a line having its y-intercept at the point
and its <em>x</em>-intercept at the point
. Then, imagine that the segment of the line where
to be reflected along the <em>x</em>-axis, and you get the graph of the absolute function
.
Consider the inequality
,
this statement can actually be conceptualise as the question
.
Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).
- Case 1 (when
)
- Case 2 (when
)
*remember to flip the inequality sign when multiplying or dividing by
negative numbers on both sides of the statement.
Therefore, the values of <em>x</em> that satisfy this inequality lie within the interval
.
Similarly, on the real number line, the interval is shown below.
The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.
