Once upon a time in a totally real kingdom a girl named Anel

Once upon a time, in a totally real kingdom, a girl named Anela saved the King’s son from eating a poisoned pear. In response, the King granted Anela anything she wanted. Anela told the King: “AllI want is a penny today. Then, for the rest of the month, each day I want you to give me twice as many pennies as you gave me the day before.” The King granted Anela’s request, thinking that he had gotten the better end of the deal, and secretly hi-ved himself when no one was looking. In answering the following questions, assume that the day that Anela got the rst penny is day zero, the next day is day 1, etc., and that there are 30 additional days remaining in the month.

(a) How many pennies will Anela receive on day 5?

(b) How many pennies will Anela receive on day 10?

(c) The amount of pennies Anela receives each day (after day 0) is what percent of the amount of pennies received on the previous day?

(d) Write a function describing how many pennies Anela will receive on the nth day. Make sure to dene any variables you have used.

(e) Explain how your answers from parts (c) and (d) relate.

(f) Describe the domain and range of your function from part (d). Also describe how your function changes over time, with an emphasis on the rate of change (slope) of your function. Example: Is it positive? Negative? Both at dierent times? Is it constant? Is it changing? How?

(g) Do you think that the King got the better deal, or do you think that Anela got the better deal? Explain and provide evidence for why you think what you do.

Solution

AllI want is a penny today. Then, for the rest of the month, each day I want you to give me twice as many pennies as you gave me the day before.

Pennied she recieved : 0 , 1 , 2, 4, 8 , 16 , 32 , 64, 128 ,256...... and son

a) 5th day -- 8 pennies

b) 10th day : 256 pennies

c) % of pennies of the previous day : (8/4)*100 = 200%

d) Function :Its a Gemoetric progreesion with common ration of 2:

N = 1*(2)^k-2 ; k = 2.. after 1 st day when she recieved 0 penny

e) for d) common ratio is 2 and % change in part c) is 200% or 2 times

f) Domain : k >=2 : [2, 30]

Range: N >0 ; (0 , inf)