The graph of an exponential function has a y-intercept of 8 and contains the point (3,64). Find the exponential function that de
2 answers:
Given:
Y-intercept of exponential function is 8.
It contains the point (3,64).
To find:
The exponential function that describes the graph.
Solution:
The general form of an exponential function is
...(i)
where, a is initial value or y-intercept and b is growth factor.
Since, y-intercept is 8, therefore, a=8.
Put a=8 in (i).
...(ii)
It contains the point (3,64). Put x=3 and y=64.
Divide both sides by 8.
On comparing both sides, we get
Put b=2 in (ii).
The functions form of this equation is
Therefore, the required function is .
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Answer:
<h3>AB ≈ 70m</h3>Step-by-step explanation:
Check the attachment for the diagram.
You can see from the diagram that it is a right angled triangle with opposite side AB and adjacent side BC. Using SOH, CAH, TOA trig identity to get the length of AB. According to TOA;
tan 35° = opposite/adjacent
tan 35° = AB/BC
tan 35° = AB/100
AB = 100tan35°
AB = 100 * 0.7002
AB = 70.02m
Hence the distance across a lake between A and B is approximately 70m
