7.3.1 Does the data in the following table follow a linear or exponential growth

Question

7.3.1 Does the data in the following table follow a linear or exponential growth model? Assuming that A(t) is either a linear or exponential function, find a formula for A(t) and calculate A(5) A(t) 10 13 7.3.2 Does the data in the following table follow a linear or exponential growth model? Assuming that A(t) is either a linear or exponential function, find a formula for A(t) and calculate A(3) A(t) 18 54 7.3.3 Does the data in the following table follow a linear or exponential growth model? Assuming that A(t) is either a linear or exponential function, find a formula for A(t) and calculate A(4) A(t) 40 20 10 -3

Explanation / Answer

7.3.1

the data shown in the table is of linear model

slope = 7-4 /1- 0

= 3

hence, linear model is

A(t) = 3t + 4

A(3) = 3(3) + 4 = 13

7.3.2

the data shown in the table is expnential

finding the formula

6 = ab^-1

18 = ab^2

dividing the two equations

b^3 = 3

b = 1.442

a = 8.656

hence , function is

A(t) = 8.656 ( 1.442)^t

A(3) =  8.656 ( 1.442)^3

A(3) = 26

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