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Given:
The price of bananas can be determined by the equation P=0.25n, where P is the price and n is the number of bananas.
To find:
The constant of proportionality
Solution:
We have,
...(i)
where P is the price and n is the number of bananas.
Price P is directly proportional to the number of bananas. So,
...(ii)
Where, k is the constant of proportionality.
On comparing (i) and (ii), we get
Therefore, the constant of proportionality is 0.25.
I graphed the given points and based on my graph.
<span> x y </span>→ EXPONENTIAL<span><span>
</span> <span> -2 21
</span><span> 1 4
</span><span> 0 1
</span><span> 1 0
</span></span><span> x y </span>→ LINEAR<span><span>
</span> <span> -2 6
</span> <span> -1 -2
</span><span> 0 2
</span><span> 1 6
</span></span>
<span> x y </span>→ QUADRATIC<span><span>
</span> <span> -2 12
</span> <span> -1 -2
</span><span> 0 -8
</span><span> 1 -6
</span></span><span> <span><span> x y </span></span></span>→ EXPONENTIAL<span><span><span>
</span> <span> -2 16
</span> <span> -1 8
</span><span> 0 4
</span><span> 1 2
LINEAR FUNCTIONS always maintain a constant slope. In the above linear function, the slope is 4.
EXPONENTIAL and QUADRATIC FUNCTIONS have different slope in every point.
Exponential functions can be identified by the immediate increase or decrease in the value of y resulting to a minimal increase or decrease in the value of x.
Quadratic functions can be identified as such due to the similar points it has after having the vertex.
</span></span></span>
<span> x y </span>→ EXPONENTIAL<span><span>
</span> <span> -2 21
</span><span> 1 4
</span><span> 0 1
</span><span> 1 0
</span></span><span> x y </span>→ LINEAR<span><span>
</span> <span> -2 6
</span> <span> -1 -2
</span><span> 0 2
</span><span> 1 6
</span></span>
<span> x y </span>→ QUADRATIC<span><span>
</span> <span> -2 12
</span> <span> -1 -2
</span><span> 0 -8
</span><span> 1 -6
</span></span><span> <span><span> x y </span></span></span>→ EXPONENTIAL<span><span><span>
</span> <span> -2 16
</span> <span> -1 8
</span><span> 0 4
</span><span> 1 2
LINEAR FUNCTIONS always maintain a constant slope. In the above linear function, the slope is 4.
EXPONENTIAL and QUADRATIC FUNCTIONS have different slope in every point.
Exponential functions can be identified by the immediate increase or decrease in the value of y resulting to a minimal increase or decrease in the value of x.
Quadratic functions can be identified as such due to the similar points it has after having the vertex.
</span></span></span>