The “Magic Penny” Problem

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Presentation transcript:

The “Magic Penny” Problem Suppose that I give you a “Magic Penny” which doubles in value each day. What will be its value at the end of the 1st week? What will be its value at the end of the 2nd week? What will be its value at the end of the month? (hint: It’s easier to generalize a formula than to fill out the calendar)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 3) 4) 5) 6) 7) ? 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4) 5) 6) 7) ? 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 5) 6) 7) ? 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 6) 7) ? 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 7) ? 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) ? 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) 128¢ 9) 10) 11) 12) 13) 14) ? 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) $1.28 9) 10) 11) 12) 13) 14) ? 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) $1.28 9) $2.56 10) 11) 12) 13) 14) ? 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) $1.28 9) $2.56 10) $5.12 11) 12) 13) 14) ? 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) $1.28 9) $2.56 10) $5.12 11) $10.24 12) 13) 14) ? 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) $1.28 9) $2.56 10) $5.12 11) $10.24 12) $20.48 13) 14) ? 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) $1.28 9) $2.56 10) $5.12 11) $10.24 12) $20.48 13) $40.96 14) ? 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) ) 128¢ 9) $2.56 10) $5.12 11) $10.24 12) $20.48 13) $40.96 14) $81.92 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31)

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 2¢ 3) 4¢ 4) 8¢ 5) 16¢ 6) 32¢ 7) 64¢ 8) 128¢ 9) $2.56 10) $5.12 11) $10.24 12) $20.48 13) $40.96 14) $81.92 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) ?

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 21 ¢ 3) 22 ¢ 4) 23 ¢ 5) 24 ¢ 6) 25 ¢ 7) 26 ¢ 8) 27 ¢ 9) 28 ¢ 10) 29 ¢ 11) 210 ¢ 12) 211 ¢ 13) 212 ¢ 14) 213 ¢ 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 2? ¢

The “Magic Penny” Problem Sunday Monday Tuesday Wed. Thursday Friday Saturday 1) 1¢ 2) 21 ¢ 3) 22 ¢ 4) 23 ¢ 5) 24 ¢ 6) 25 ¢ 7) 26 ¢ 8) 27 ¢ 9) 28 ¢ 10) 29 ¢ 11) 210 ¢ 12) 211 ¢ 13) 212 ¢ 14) 213 ¢ 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 231-1¢ = 230¢ = $10,737,418.24