Question

the exponential model below represents the population of an animal ( x ) years from now. what is meaning of 2685 in the model?
f(x) = 2685(1.07)^x
show your work here

• the animal will have doubled in population after 2685 years
• the animals population today is 2685
• every year, the animal decreases in population by 2685
• every year, the animal increases in population by 2685
• the animals population will be zero after 2685 years

Explanation:

Step1: Define current time (x=0)

To find the initial population, substitute $x=0$ into the model.

Step2: Evaluate the exponential term

Any number to the power of 0 is 1: $1.07^0 = 1$

Step3: Calculate initial population

$f(0) = 2685 \times 1 = 2685$

Step4: Eliminate incorrect options

• The model shows growth ($1.07>1$), so decrease options are wrong.
• 2685 is not a time value, so time-based options are wrong.

Answer:

The animal's population today is 2685