THE AVERAGE WEIGHT W (IN POUNDS) OF AN ATLANTIC COD AGED t YEARS CAN BE MODELED BY THE EGUATION W=1.16(1.44)^t.
FIND THE RATIO OF THE WEIGHT OF A 5 YEAR OLD COD TO THE WEIGHT OF A 2 YEAR OLD COD. EXPRESS THIS RATIO AS A POWER OF 1.44!!!!!!
HOW WOULD I DO THIS???
PLEASE HELP!!!!!!!
weight of a 5 year old cod = 1.16(1.44)^5
weight of a 2 year old cod = 1.16(1.44)^2
so when we form the ratio (1.16(1.44)^5):(1.16(1.44)^2) it reduces to
(1.44^3):1
To find the ratio of the weight of a 5 year old cod to the weight of a 2 year old cod, you can substitute the values of t into the equation and evaluate the ratio.
Let's start by finding the weight of a 5 year old cod.
Substitute t = 5 into the equation:
W = 1.16(1.44)^t
W = 1.16(1.44)^5
W = 1.16(5.31441)
W ≈ 6.1636
Now, let's find the weight of a 2 year old cod.
Substitute t = 2 into the equation:
W = 1.16(1.44)^t
W = 1.16(1.44)^2
W = 1.16(2.0736)
W ≈ 2.4054
To find the ratio, divide the weight of the 5 year old cod by the weight of the 2 year old cod:
Ratio = Weight of 5 year old cod / Weight of 2 year old cod
Ratio = 6.1636 / 2.4054
Ratio ≈ 2.5634
Since we want to express the ratio as a power of 1.44, we need to find the exponent to which 1.44 should be raised to achieve this ratio.
Let's call the exponent x:
1.44^x = 2.5634
To solve for x, you can take the logarithm of both sides of the equation. In this case, we will use the logarithm base 1.44:
log base 1.44 (1.44^x) = log base 1.44 (2.5634)
Simplifying the equation using the logarithmic property:
x = log base 1.44 (2.5634)
Using a calculator, calculate the logarithm value:
x ≈ 1.779
Therefore, the ratio of the weight of a 5 year old cod to the weight of a 2 year old cod can be expressed as 1.44^1.779.