71-73classwork open Notes, open Book, Groups and calculators allowed. Due at end

Question

71-73classwork open Notes, open Book, Groups and calculators allowed. Due at end of class today. Block Pledge. 1. The amount of bitcoins in circulation has grown 30% every year. There were 10.000 bitcoins a write a function for the number of bitcoins at any time, t in years) b How many bitcoins are in circulation after 5 years? 2. Afloating iceberg has trapped a population of Adele penquins who must now travel hundreds of miles to the sea to feed. Initially, there were 240,000 penguins in the colony. Each year, the population has decreased 20%. a. Write a function for the number of penguins remaining. b. How many penguins will there be after 10 years (if the iceberg doesn't move away). 3. Solve the equation. a. 3 +2 35x 4 b. 3 (9)

Explanation / Answer

(b) The number of bitcoins after 5 years is f(6) = 10000*(1.3)5 = 10000*3.71293 =37129 ( on rounding off to the neares whole number).

2. ( a) There were 240000 penguins initially.The number of penguins in the succeeding years are 240000*0.8, 240000*(0.8)2,…… The t th term of this geometric series is f(t) = 240000*(0.8)t-1 which is the number of penguins remaining in the t th year.

b. The number of penguins after 10 years is f(11) = 240000*(0.8)10 = 240000*0.107374182 = 25770 (on rounding off to the neares whole number).

3.( a) 3x+2 = 35x-4. Hence x+2 = 5x-4 or, 5x-x = 2+4 or, 4x = 6 so that x = 6/4 = 3/2 or,1.5.

(b). 3x+4 = 9x = (32)x = 32x . Hence x+4 = 2x or, 2x-x = 4 i.e. x = 4.

4.    A general exponential function is y = abx . If the graph of this function passes through the points   (0,3.1) and (4,4017.6), then 3.1 = ab0 or, a = 3.1…(1) and 4017.6 = ab4 = (3.1)b4 or, b4 = 4017.6/3.1 = 1296 so that b = (1296)1/4 = 6. Thus, the required exponential function is y = (3.1)* 6x .

5. The formula for compound interest ( compounded weekly) is M = P(1+r/52)52t where P is the principal, M is the maturity value, r is the rate of interest in decimals and t is the number of years. Here, P = $ 8200 , t = 11 and r   = 5.6/100 = 0.056. Therefore, M = 8200 ( 1+ 0.056/52)52*11 = 8200(1.00176923077)572 = 8200*2.748637638 = 22538.82863 = $ 22538.88 ( on rounding off to the nearest cent).

             

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.