Question

A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7bt, where t is the time in weeks after the release and b is a positive unknown base. After observing the population growth over a few weeks, the exponential function P(t) = 7(2)t is used to model the growth. Interpret the significance of 2 in the function as it applies to the situation.

Answer 1

A. the population is doubling each week

Explanation:

got it right

Answer 2

b is the base of function which help us to determine the growth rate and Also tells the multiplicity of fishes .

Explanation:

Exponential Function:
`ab^x` --1

a = initial value (the amount before measuring growth or decay)

b>1 growth

b<1 decay

The growth "rate" (r) is determined as b = 1 + r.

The decay "rate" (r) is determined as b = 1 - r

After observing the population growth over a few weeks, the exponential function :

`P(t) = 7(2)^t`

Comparing it with 1

b = 2

Since b >1

So, it is the growth function

So, The growth "rate" (r) is determined as b = 1 + r.

2 = 1+r

r = 1

Hence growth rate is 1

So, b is the base of function which help us to determine the growth rate and Also tells the multiplicity of fishes .