Question

Find the exponential function that satisfies the given conditions: Initial value = 37, increasing at a rate of 5% per year

Answer 1

The required function is:

Option 3: $f(t) = 37. (1.05)^t$

Step-by-step explanation:

The initial value and rate is used to write exponential function

Here

Given

Initial value = 37

Rate = r = 5%

When the rate is 5%, the next year the quantity will be 1+0.05 = 1.05 time of the current quantity.

So,

The function can be written as:

$f(t) = 37. (1.05)^t$

For initial value, put t=0

$f(t) = 37. (1.05)^0\\f(t) = 37 * 1\\f(t) = 37$

Hence,

The required function is:

Option 3: $f(t) = 37. (1.05)^t$

Keywords: Functions, exponential functions

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