Which exponential function has the greatest average rate of change over the interval [ 0 , 2 ]
1 answer:
The exponential function which has the greatest average rate of change over the interval [0, 2] is option B.
<h3>How to calculate the average rate of change?</h3>Mathematically, the average rate of change between two (2) points can be calculated by using this expression;
For option A, we have:
when x = 0; when x = 2;
y = 3(1.6)^x y = 3(1.6)^x
y = 3(1.6)^0 y = 3(1.6)^2
y = 3. y = 7.68
ΔA = (7.68 - 3)/(2 -0) = 2.34.
For option B, we have:
ΔA = (9 - 4)/(2 -0) = 2.5.
For option C, the exponential function has a common ratio of 2.
ΔA = 2.
For option D, we have:
ΔA = (10 - 8)/(1 -0) = 2.
In conclusion, we can logically deduce that the exponential function which has the greatest average rate of change over the interval [0, 2] is option B i.e 2.5.
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The reasonable estimate of the current customer price index is 195. The option B is the correct option.
<h3>Customer price index</h3>Customer price index is the price index which measures the weight average of price of basket of customers goods or services.
It can be given as,
Here is the cost of market basket in current period and
is the cost of market basket in the base period.
Cost of market basket in current period is
Cost of market basket in 1983 is,
Substitute all the values in the formula
Thus the value of current CPI is 168.5 which is near about the 170.
Hence, the reasonable estimate of the current customer price index is 195. The option B is the correct option.
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