A) The exponential model is y = 5*3ˣ
B) The predicted population of squid in 2031 is 3.09 x 10¹⁵.
The predicted population is too large to compared to the population of squid in the table. so this cannot be accurate.
What is exponential function?
An exponential function can be represented by
y = abˣ
where,
The exponent, x represents the power to which the base (b) is raised
The base, b of the exponential function, is a constant greater than 0 and not equal to 1.
The coefficient or amplitude,a, is a constant multiplier affecting the overall scale of the function.
The exponent (x) determines the position on the x-axis, the base (b) governs the rate of growth or decay, and the coefficient (a) scales the entire function.
From the table
when x = 0
the population is 5, meaning that the constant multipler a = 5
b is the constant ratio population ot
t = 0, 5 and t = 3, 15
b = ratio = 15/5 = 3
So, the exponential function is
y = 5*3ˣ
Part B
To predict the population of the squid in 2031
The value of x = 31
Substitute into the exponential model
y = 5*3ˣ
y = 5*3³¹
= 3.09 x 10¹⁵
Therefore, owning to the given that data and the exponential model, the predicted population is too large to compared to the population of squid in the table. so this cannot be accurate.