The maximum length of a certain type of fish is 65 centimeters. The difference between the maximum length and the length at age years is given by $D = 61.75 \times 0.82 ^ { t }$ centimeters. Write a for-
Mula that gives the length L , in centimeters, of the fish at age years.
A) $L = 65 + 61.75 \times 0.82 ^ { t}$
B) $L = 65 - 61.75 \times 0.82 ^ { t }$
C) $L = 65 \times 61.75 \times 0.82 ^ { t }$
D) $L = 61.75 \times 0.82 ^ { t } - 65$

Question

The maximum length of a certain type of fish is 65 centimeters. The difference between the maximum length and the length at age  years is given by $D = 61.75 \times 0.82 ^ { t }$ centimeters. Write a for-
Mula that gives the length L , in centimeters, of the fish at age  years. 
A) $L = 65 + 61.75 \times 0.82 ^ { t}$ 
B) $L = 65 - 61.75 \times 0.82 ^ { t }$ 
C) $L = 65 \times 61.75 \times 0.82 ^ { t }$ 
D) $L = 61.75 \times 0.82 ^ { t } - 65$

Quizplus · Accepted Answer

The difference between the maximum length and length at age 11 is given by $D = 61.75 \times 0.82 ^ { t }$ centimeters. 
Therefore, the length at age 11 would be: 
$L_{11} = 65 - D = 65 - 61.75 \times 0.82 ^ { 0 }$ 
Simplifying the above equation, we get: 
$L_{11} = 65 - 61.75 = 3.25$

This means that the fish starts at a length of 3.25 centimeters at age 11. 
To find the length L at any age beyond 11 years, we simply add the growth component to the starting length, so the formula is:

$L = 3.25 + 61.75 \times 0.82 ^ { t }$

Now, replacing 3.25 with 65 in the above formula, we get:

$L = 65 - 61.75 \times 0.82 ^ { t }$

Therefore, the correct choice is B.

The Maximum Length of a Certain Type of Fish Is D=61.75×0.82tD = 61.75 \times 0.82 ^ { t }D=61.75×0.82t

The Maximum Length of a Certain Type of Fish Is $D = 61.75 \times 0.82 ^ { t }$