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


f(t) = 37 ⋅ 5t

f(t) = 5 ⋅ 1.05t

f(t) = 37 ⋅ 1.05t

f(t) = 37 ⋅ 0.05t

Respuesta :

absor201

The required function is:

Option 3: [tex]f(t) = 37. (1.05)^t[/tex]

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:

[tex]f(t) = 37. (1.05)^t[/tex]

For initial value, put t=0

[tex]f(t) = 37. (1.05)^0\\f(t) = 37 * 1\\f(t) = 37[/tex]

Hence,

The required function is:

Option 3: [tex]f(t) = 37. (1.05)^t[/tex]

Keywords: Functions, exponential functions

Learn more about functions at:

  • brainly.com/question/11280112
  • brainly.com/question/11286417

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