Answer:
15,267
Step-by-step explanation:
To solve this problem, lets use the exponential growth formula which is:
A = total amount
P = original amount
r = growth rate (decimal)
t = years
<u>Before we plug in the values, don't forget to change 3.5% to its decimal form.</u>
3.5% -> -> 0.035
Lets plug in the values:
The population after 7 years will be 15,267.
Answer:
The midpoint is
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
we have
substitute
Answer:
Step-by-step explanation:
These are the transformations of interest:
g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k
g(x) = f(x) +k . . . . vertical translation by k units (upward)
g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis
g(x) = f(x-k) . . . . . horizontal translation to the right by k units
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Here, we have ...
g(x) = 1/3f(-1/3(x+1)) +3
The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:
_____
<em>Additional comment</em>
The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.
The horizontal transformations could also be described as ...
The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.
