Question

Step by step

A fisherman illegally drops some fish into a pond, and they quickly propagate (reproduce). The population
growth of the new specifies is modeled by P(x) =6(b)^x where x is the time in weeks following the moment
he dropped the fish into the pond and b is a positive unknown base. Suppose that b is 3. Graph this
relationship. How long does it take for there to be at least 100 fish in the pond?

Answer 1

C. About 6 days

Explanation:

Here the function that shows the population of fish after x weeks,

Where b is any unknown,

If b = 3,

Then, the function is,

Which is a exponentially increasing function,

That having y-intercept = (0,1)

And, horizontal asymptote,

y = 0

End behavior of the function:

As ,

As ,

Thus, by the above information we can graph the given relation.

Now, For at least 100 fish in the pound,

By taking log on both sides,

Thus, after 0.8567 weeks (approx) the fish on the pound will be at least 100.

1 week = 7 days,

0.8567 weeks = 5.9969 days ≈ 6 days

Hence, after 6 days (approx) the fish on the pound will be at least 100.