Option 2: [tex]f(t) = 31.(1.1)^t[/tex] is the correct answer.
Step-by-step explanation:
Let t be the independent variable time and f(t) be the function that will be used to represent the exponential growth
The general form of an exponential function is given by:
[tex]y = a(1+r)^t[/tex]
Here
a is the initial value of the function while r is the growth rate
and t is the number of years
Given
Initial value = 31
Growth rate = 10% per year
We have to convert the growth rate in decimal
So,
[tex]r = \frac{10}{100} = 0.1[/tex]
Putting the values in the general form
[tex]f(t) = 31 . (1+0.1)^t\\f(t) = 31 . (1.1)^t[/tex]
Hence,
Option 2: [tex]f(t) = 31.(1.1)^t[/tex] is the correct answer.
Keywords: Functions, exponential functions
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