Question

The function f(x)=65000(1.5)^x can be modeled the population of a city for x, the number of years that have passed since 2010. what inequality represents the reasonable range of the function based on the situation.​

Answer 1

Answer:

Here is your answer dear have a brilliant day

Answer 2

The function f(x)=65000(1.5)ˣ   modeled the population of a city for x, the number of years that have passed since 2010. Inequality represents the reasonable range of the function based on the situation is f(x) ≥ 65000

Given function

f(x)=65000(1.5)ˣ

x, the number of years that have passed since 2010.

if talk about only non negative values of x  as number passes 2010 is given.

Then for x = 0

f(x) = 65000(1.5)⁰ = 65000

Further as value of x increases then

Value of f(x) increases

Every year population gets 1.5 times of previous years

Hence for x→ ∞  , f(x)→∞

Hence f(x) = [65000 , ∞)  for  x ∈ [0 , ∞)

Hence  f(x) = [65000 , ∞) can be represented as inequality

f(x) ≥ 65000

Inequality f(x) ≥ 65000 represents the reasonable range of the function.

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