Answer: 107.5%
Step-by-step explanation:
The explicit exponential model for growth :
[tex]A=A_0(1+r)^t[/tex] (1), where [tex]A_0[/tex] is the initial amount and r is the rate of interest and t is the time.
Given : Suppose a fish population is currently 2800 and 3 years later the population is 25000.
i.e. [tex]A_0=2800[/tex]
Put [tex]A_0=2800[/tex], A = 25000 and t=3 in (1)
[tex]25000=2800(1+r)^3\\\\ (1+r)^3=\dfrac{25000}{2800}=8.92857142857\approx8.93[/tex]
Taking cube root on both sides , we get
[tex]1+r=(8.93)^{1/3}=2.07467697105\approx2.075\\\\ r=2.075-1=1.075=107.5\%[/tex]
Hence, the rate of growth = 107.5%
The rate of growth of the fish using the explicit exponential model in percentage is 107.5 %.
Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
Suppose a fish population is currently 2800 and 3 years later the population is 25000.
The explicit model is given as
[tex]\rm A = A_o (1+r)^t[/tex]
Where A₀ is the initial population of fish, t be the time and r be the rate.
We have
A₀ = 2800
A = 25000
t = 3
Then the equation will be
[tex]\rm 25000= 2800(1+r)^3[/tex]
On simplifying, we have
[tex]\begin{aligned} 8.9286 &= (1+r)^3\\\\1+r &= 2.07457\\\\r &= 1.07457 \approx 1.075 \\\\r &= 107.5 \% \end{aligned}[/tex]
More about the exponent link is given below.
https://brainly.com/question/5497425
