Final answer:
The function for the number of tigers (T) after each year (Y) is T(Y) = 7 + (7 * 0.1 * Y). The function for the number of eagles (E) after each year (Y) is E(Y) = 15 + 2 * Y.
After 10 years, there will be 14 tigers and 35 eagles at the zoo.
The number of tigers and eagles will never be the same.
Step-by-step explanation:
Part A:
To write functions to represent the number of tigers and eagles at the zoo throughout the years, we need to determine the growth pattern for each species.
For tigers, the number increases by 10% each year. Let's assume the initial number of tigers is 7. The function for the number of tigers (T) after each year (Y) can be represented as:
T(Y) = 7 + (7 * 0.1 * Y)
For eagles, 2 new eagles join the zoo every year. Let's assume the initial number of eagles is 15. The function for the number of eagles (E) after each year (Y) can be represented as:
E(Y) = 15 + 2 * Y
Part B:
To find the number of tigers after 10 years, we can substitute Y = 10 in the tiger function:
T(10) = 7 + (7 * 0.1 * 10) = 7 + 7 = 14
So, there will be 14 tigers at the zoo after 10 years.
To find the number of eagles after 10 years, we can substitute Y = 10 in the eagle function:
E(10) = 15 + 2 * 10 = 15 + 20 = 35
So, there will be 35 eagles at the zoo after 10 years.
Part C:
To find the approximate number of years when the number of tigers and eagles is the same, we can set the two functions equal to each other and solve for Y:
7 + (7 * 0.1 * Y) = 15 + 2 * Y
0.1 * Y - 2 * Y = 15 - 7
-1.9 * Y = 8
Y = 8 / -1.9
Y ≈ -4.211
Since time cannot be negative, we can disregard this result. Therefore, the number of tigers and eagles will not be the same.