Question

A scientist measured the energy of a system and found that it was increasing. The data shown represent the energy taken every billionth of a second. Time (nanoseconds) 0 1 2 3 Energy (Joules) 2.654 6.290 14.909 35.335 Classify the type of growth the scientist observed. 1)linear 2)quadratic 4)exponential 5)logarithmic

Answer 1

At start ( t = 0 nanoseconds ) :

E ( t = 0 ) = 2.645 J

E ( t = 1 ) = 6.290 J

E ( t = 1 ) : E ( t = 0 ) = 6.290 : 2.645 = 2.37

Also:

E ( t = 2 ) : E ( t = 1 ) = 14.909 : 6.290 = 2.37

E ( t = 3 ) ; E ( t = 2 ) = 35.335 : 14.909 = 2.37

E ( t ) = 2.645 * 2.37 ^ t

The answer is 4) exponential growth.

Answer 2

At start ( t = 0 nanoseconds ) :

E ( t = 0 ) = 2.645 J

E ( t = 1 ) = 6.290 J

E ( t = 1 ) : E ( t = 0 ) = 6.290 : 2.645 = 2.37

Also:

E ( t = 2 ) : E ( t = 1 ) = 14.909 : 6.290 = 2.37

E ( t = 3 ) ; E ( t = 2 ) = 35.335 : 14.909 = 2.37

Therefore, the formula for calculating the energy of the system is:

E ( t ) = 2.645 * 2.37 ^ t

The answer is 4) exponential growth.