less 5.2.4 semester 1 practice- Mathematics PDF

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Journal page for Lesson 5.2.4 Semester 1 Mathematics. Covers all questions and shows work with steps....

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Dymone Moore Dec 9, 2021 Mathematics 5.2.4 Modeling Exponential Functions

Choosing a Valuble Coin Alex colects coins that appreciate (increase in) value . At the store he has found three coins that he can afford Help Alex decide which coin to buy by selecting two coins and comparing their values over time. 1. Which two coins are you going to compare ? Circle the two coins you picked. Coin B and Coin C 2.What are the current values and appreciaation rates of the two coins we selected? (2 points: 1 point for each of two coins) Coin B C

Curent Value $40 $60

Annual Appreciation Rate 5% 4%

3.Write an exponential equation for each coin that will give the coin's value, V at time, t. Use the formula: V(t) = P(1 + r) where V(t) = value of the coin in t years, P = initial investment, and r= the growth rate For each of the coins selected , P and then set up an equation to the value of the coin at any time t( 2 points: 1 point for each coin)

Coin B C

p $40 $60

r 5% 4%

Function V(t)= 40(1 + 0.05) t V(t)= 60(1 + 0.04) t

4.In the coin value formula V(t) = A * (1 + r) ^ t which part (s) form the base of the exponential function ? Which part (s) form the constant , or initial value ? Which part (s) form the exponent ? (4 points point for each answer below ) Base: (1+r) Constant or initial value: P Exponent: t In this function the value of r were to increase , would the value represented by P also increase or stay the same? Why? Explain your answer using terms such as growth and initial value in the context of the coin problem. The Initial value, P, Is constant and will stay the same. The rate of growth, r, makes the value, V(t) increase over time, t.

5.Find the value of the coins after 10, 20, 30 , and 60 years. Use the function you in question 3 to calculate the value. (points 1 point for each time interval Coin A Initial Value 10 Years 20 years 30 years 60 years B: V(t)= 40(1 + .05)t = 40(1.05)t V(10) = 40(1.05)10 ≈ 40 (1.629)

Coin B $40 $65.16 $106.13 $172.88 $747.17

Coin C $50 $74.01 $109.56 $162.17 $525.98

C: V(t) = 50(1 + .04)t = 50(1.04)t V(10) = 50 (1.04) 10 ≈ 50 (1.480)

≈ $65.16

V(20) = 40(1.05) 20 ≈ 40(2.653) ≈ $106.13

V(10) = 40(1.05)30 ≈ 40(4.322) ≈ $172.88 V(10) = 40(1.05)60 ≈ 40(18.679) ≈ $747.17

≈ $74.01

V(20) = 50(1.04) ≈ 50(2.191) ≈ $109.56

V(10) = 50(1.04)30 ≈ 50(3.243) $162.67 V(10) = 40(1.04)60 ≈ 50(10.520) ≈ $525.98

6.Which coin is more valuable after 10 years? 20 years? years? 60 years? Which coin would you purchase if you intended to keep it longer than 60 years, and why? Hint Look at r After 10 & 20 years coin C is worth more. After 30 & 60 years coin B is worth more. Coin B had a rate of 5%, while coin C had a rate of 4%. So, by keeping the coins longer, the one with the bigger rate wil be worth more money....