A waterfall has a height of 1400 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 12 feet p
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Given:
The graph of an exponential function.
To find:
The exponential growth factor as x increases by 1 unit.
Solution:
From the given graph, it is clear that the exponential function passes through the points (1,1) and (3,9). So, the equation of the exponential must must be satisfy by these points.
The general exponential function is:
...(i)
Where, a is the initial value and b is the growth factor.
Putting in (i), we get
...(ii)
Putting in (i), we get
...(iii)
Divide (iii) by (ii).
b is the the growth factor and the value of b is 3.
Therefore, the exponential growth factor is 3 as x increases by 1 unit.