Simplify 3/4 ÷ 9/8 ( write answer as a fraction)
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We are given, cost of the robot for 0 number of year = $16,000.
0 represents initial time of the robot.
After 10 year cost of the robot is = $0
The problem is about the number of the years and cost of the robot over different number of years.
So, we could take x coordinate by number of hours and y coordinate for y number of hours.
So, from the problem, we could make two coordinates for the given situation.
(x1,y1) = (0, 16000) and (x2,y2) = (10, 0).
In order to find the function of time, we need to find the rate at which robot rate depreciates each year.
Slope is the rate of change.
So, we need to find the slope of the two coordinates we wrote above.
We know, slope formula
Plugging values in formula, we get
Brecasue of depreciation we got a negative number for slope or rate of change.
Therefore, rate of depreciation is $1600 per year.
We already given inital cost, that is $16,000.
So, we can setup an a function
f(x) = -1600x + 16000.
But the problem is asked to take the variable t for time.
Replacing x by t, we get
f(t) = -1600t + 16000.
Answer: Third option.
Step-by-step explanation:
By definition, Exponential functions have the following form:
Where "b" is the base ( and
), "a" is a coefficient (
) and "x" is the exponent.
It is importat to remember that the "Zero exponent rule" states that any base with an exponent of 0 is equal to 1.
Then, for an input value 0 () the output value (value of "y") of the set of ordered pairs that could be generated by an exponential function must be 1 (
).
You can observe in the Third option shown in the image that when ,
Therefore, the set of ordered pairs that could be generated by an exponential function is the set shown in the Third option.