Question

once upon a time in a nice community of 21000 residents, a mutated beetle bit one of the local teenagers. the teenager freaked out after a day and started biting people and infecting them too. the teenager would bite on average 4 people a day. one day after being bitten, those people would begin biting people and would bite at least 4 people a day as well. after a while, the town no longer had any normal people and the military had to come in to destroy all of the mutants.the initial number of mutants is 1.the number of mutants increases at a factor of 5 each day.function to model number of mutants: $f(x) = 5^x$

Explanation:

Step1: Define initial condition

Initial mutants $f(0)=1$

Step2: Identify growth factor

Daily growth factor = 5

Step3: Formulate exponential function

General form: $f(x) = \text{Initial value} \times (\text{Growth factor})^x$
Substitute values: $f(x) = 1 \times 5^x = 5^x$

Answer:

$f(x) = 5^x$