Question

Question 12 Approximate the following data with an exponential function and find the value of the function for 7 2 4 50) 3.62 5.63 8.83 13.62 21.22 a) O38.49 b) Q55.34 c) O51.42 d) O42.51 e) 049.38

Answer 1

Basic formula-  where the constant A is the initial value of x, the constant b is a positive growth factor, and τ is the time constant—the time required for x to increase by one factor of b: If τ > 0 and b > 1, then x has exponential growth.

In our case here, with every time factor, values are increasing wit approximately 64.18% of the previous value.

Eg- f(1)/f(2) = 3.62/5.63 = 0.642 = 64 % appx

value at f(6) can be calculated by using percentage basics, i.e. what will be the future value if present value increases by 64%

f(6) = 21.22*1.64 = 34.80

similarly,

f(7) = 34.80*1.64 = 57.07

hene, the option B will be our answer if we approximate our values.