Comparing Exponential and Linear Growth 1. You are a star basketball player and

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Comparing Exponential and Linear Growth 1. You are a star basketball player and receive the following two offers. Which one should you choose? (There are 82 regular season games in the NBA.) » A one billion dollar signing bonus and 1 million dollars per game. > A one penny signing bonus with salary to double each game. In other words the salary for the first game is 2 pennies, the salary for the second game is 4 pennies, and so on. 2. At time t 0 years, a species of turtle is released into a wetland. when t = 4 years, a biologist estimates there are 300 turtles in the wetland. Three years later, the biologist estimates there are 450 turtles. Let P represent the size of the turtle population in year t a. Find a formula for P=f(t) assuming linear growth. Interpret the parameters of your formula in terms of the turtle population. b. Find a formula for P=g(t) assuming exponential growth. Interpret the parameters of your formula in terms of the turtle population. c.Inyear t = 12, the biologist estimates that there are 900 turtles in the wetland., What does this indicate about the two population models? Assignment

Explanation / Answer

1) there are two points

( 4 , 300 ) and ( 7 , 450 )

assuming the growth to be linear

slope = ( 450 - 300 ) / (7 - 4)

= 50

y - 300 = 50 ( x - 4)

y = 50x + 100

formula is f(t) = 50t + 100

b) finding growth to be exponetial

y = ab^t

300 = ab^4

450 = ab^7

dividing the two equations

b^3 = 450/300

b = 1.1447

a = 174.72

hence, exponential function is

g(t) = 174.72 (1.1447)^t

c) in the year t = 12

population of turtles according to linear model is

f(t) = 50(12) + 100 = 700

according to exponential model

g(t) = 174.72 (1.1447)^12

g(t) = 885

this indicates the exponential model is more accurate

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