<span>8.0936752e+14 is the answer</span>
Just find the intervals in between the numbers
As 1 inch = 2.54 cm.
As Annalisa is 64 inches tall,
so the height of Annalisa in centimeter = 64 x 2.54 cm = 162.5 cm (approximately).
Stefen is about 7.5 centimeters taller than Annalisa,
So, height of Stefen in centimeter= 162.5+7.5=170 cm.
and the height of Stefen in inches = 170/ 2.54 cm= 67 inches (approximately).
Keiko is about 1.5 inches shorter than Stefen,
So, the height of Keiko in inches= 67-1.5=65.5 inches.
and the height of Keiko in centimeter = 71.5 x 2.54 cm= 166.5 cm (approximately).
Hence, Annalisa is 64 inches or about 162.5 cm tall.
Stefan is about 67 inches or about 170 cm tall.
Keiko is about 65.5 inches or about 166.5 cm tall.
We can let t represent the number of months that have passed. Let's observe first what happens with number of birds and trees for the first 3 months to better understand the function that we'll create.
For the birds in the aviary, since the number decreases by 7%, for the first month it will have 93% of the original number. For the second month, the number of birds left will be 93% of what was left from the first month as shown below.
1st month | B(1) = 0.93(975)
2nd month| B(2) = 0.93[0.93(975)] = 0.93²(975)
3rd month| B(3) = 0.93[0.93²(975)] = 0.93³(975)
From this, we can see where the pattern is going and conclude that after t months, there will be B(t) = 0.93ᵗ(975) birds present.
We'll use the same approach to estimate the number of trees after t months in the aviary.
T(1) = 350 - 7
T(2) = 350 - 7 - 7 = 350 - 2(7)
T(3) = 350 - 2(7) - 7 = 350 - 3(7)
and hence,
T(t) = 350 - 7t
Thus, we have the functions for the birds and trees throughout t months.
We can now compute for the number of birds and trees present after 12 months by simply substituting 12 into our equations as shown below.
B(12) = 0.93¹²(975) = 408.13 ≈ 408
T(12) = 350 - 12(7) = 266
Hence, from this we can see that there are approximately 408 birds and 266 trees present in the aviary after 12 months.
To find the number months when there are almost the same number of trees and birds present, we can equate T(t) to B(t) and solve for the value of t. Using the graphical method, we can also find the intersection points between the two functions.
350 - 7t = 0.93ᵗ(975)
We have intersection points at around 22.21 and 44.4781. Approximating these values to whole numbers, we have 22 and 44 months.
Answers:
Part A: B(t) = 0.93ᵗ(975) and T(t) = 350 - 7t
Part B: 408 birds and 266 trees
Part C: 22 and 44 months
Reflection across the y-axis
