Write an exponential function for the set of points
1 answer:
Answer:
The function is
Step-by-step explanation:
Compare the y values. Notice that the y values are all multiples of 3 and they decrease by dividing by 3 each time. This suggests the base is 1/3.
Now check when x = 0. This is the initial value since the zero exponent gives an output of 1. So the only way for (0,27) to be a point is for 27 to e multiplied as the initial value. The function is
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To find the distance between the homes of Tom and Jimmy, it is assumed
that the distances from their home to the café are equal.
- The distance between Tom and Jimmy's home is
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Reasons:
The direction in which Tom and Jimmy walks = Towards each other
The speed at which Tom walks = 52 meters per minute
The speed with which Jimmy walks = 70 meters per minute
The time at which Tom leaves = 4 minutes earlier than Jimmy
The point at which they meet = The café
The rate of their speed = Constant
Required:
The distance between Tom and Jimmy home.
Solution:
Tom and Jimmy had a plan to walk at the same speed and meet up at the café.
We have;
The café is equal distance from Tom and Jimmy's houses.
Which gives the following simultaneous equation.
52 × (4 + t) = The distance of Tom's house from the café
70 × t = The distance of Jimmy's house from the café
- 52 × (4 + t) = 70 × t
52 × 4 = 70 × t - 52 × t = 18 × t
The time it take Jimmy to reach the café, <em>t</em> = minutes
The distance between their homes, d = 52 × (4 + t) + 70 × t
∴ d = 52 × (4 + ) + 70 ×
= 1,617.
- The distance between Tom and Jimmy's home = 1,617.
meters
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