Question

Find the exponential function that satisfies the given conditions: Initial value = 31, increasing at a rate of 10% per year

Answer 1

Option 2: $f(t) = 31.(1.1)^t$ 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:

$y = a(1+r)^t$

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,

$r = \frac{10}{100} = 0.1$

Putting the values in the general form

$f(t) = 31 . (1+0.1)^t\\f(t) = 31 . (1.1)^t$

Hence,

Option 2: $f(t) = 31.(1.1)^t$ is the correct answer.

Keywords: Functions, exponential functions

Learn more about functions at:

• brainly.com/question/9381523
• brainly.com/question/9231234

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