1. Determine the values for r and k for which the graph of y-ka passes through t

Question

1. Determine the values for r and k for which the graph of y-ka passes through the points (2.3) and (4,15) Explain in detail how you found the answer. 2. State the two key equations giving the relationships between e and In 3. A piece of paper is about 0.05 in thick. Suppose you can fold it as many times as you want, how many time would you have to fold it for the thickness to reach the moon? NOTE: use the internet to find out the conversion from inches to miles, and also the distance in miles to the moon 4. State the main features of the graph of y In 5. What are the coordinates of the reflection of the point (a,b) in the line y-? 6. Give an example of the use of logarithmic differentiation. Please choose an interesting example.

Explanation / Answer

1. y = k xr

For point (2,3), 3 = k (2)r

For point (4,15), 15 = k(4)r

Dividing them 15/3 = (4/2)r

5 = 2r

r = log25 =2.32

Subsituting back the value of r

3 = k(2)2.32

k = 0.6

Required equation is

y =0.6(x)2.32

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