Use the tables below to answer the following questions a i I

Use the tables below to answer the following questions. a. i. Initial value: ii. 1-unit growth factor: iii. 1-unit percent change: % iv. Function: b. i. Initial value: ii. 1-unit growth factor: iii. 1-unit percent change: % iv. Function:

Solution

a) i ) Intial value ( i.e value at x=0) 14

ii) x= 0 ;f(x) = 14

x =1 ;f(1) = 14.28

1 Unit growth factor =1 + ( 14.28 -14)/14 = 1.02

iii) 1 unit % change = 2 %

iv) f(x) = 14(1.02)^x

b) we can see its an exponential decay system from the data

we use the model : g(x) = a(b)^x where a = intial value and b = growth factor

271.04 = ab ----(1)

238.5152 = a(b)^2 ----(2)

Divide equation 2 by 1 : 238.5151/217.04 = b

b = 0.88 ; a = 271.04/0.88 = 308

inital value = 308

ii) 1 unit growth factor = 0.88

iii) 1 unit % change = 100 -88 = 12 %

iv) Function : g(x) = 308(0.88)^x