Question

Batman wanted to check on the population of his enemies. He noticed that initially there were 4 baddies living at Arkham asylum. Batman notices that the population doubled every 2 years. below is the equation that Batman route to predict the population of bad guys in 1992.

y=4(2)^x where x is the number of years and y is the population of bad guys.

Is Batman's equation of this scenario accurate? Explain gow you know

**please help me, i keep getting confused and second guessing myself. Thank you!!! <3**

Answer 1

Batman's equation of this scenario is not accurate.

Explanation:

The exponential function representing this situation should be

`y=a\cdot b^(nx),`

where a is the initial amount of baddies living at Arkham asylum, b is the rate at which enemies increased, n is the number determing the period of enemies increasing and x is time in years.

In your case,

a=4 (initially there were 4 baddies living at Arkham asylum),

b=2 (the population doubled),

n=1/2 (the population doubled every 2 years).

Then

`y=4\cdot 2^{(x)/(2)}.`

Note then when considering the function
`y=4\cdot 2^x` the population dubled each year, not every 2 years.