Answer:
1. initial point is (2, 4)
reflected point is (-2, 4)
the coordinates are similar because they involve the same numbers, however, with the reflection across the Y axis, the X point became negative.
2. initial point is (2, 4)
reflected point is (2, -4)
again, same numbers but the X value becomes negative
Hope this helps!
What the other person said
Answer:
1560
Step-by-step explanation:
The rate of Increase of the population (P) of the bacteria is given as:
![\frac{dP}{dt} =4.058e^{1.6t}](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D4.058e%5E%7B1.6t%7D)
![dP =4.058e^{1.6t}}dt\\Taking\: Integrals\\\int dP =4.058 \int e^{1.6t}dt\\P(t)=\frac{4.058}{1.6} (e^{1.6t} +K)\\P(t)=2.53625 (e^{1.6t} +K)](https://tex.z-dn.net/?f=dP%20%3D4.058e%5E%7B1.6t%7D%7Ddt%5C%5CTaking%5C%3A%20Integrals%5C%5C%5Cint%20dP%20%3D4.058%20%5Cint%20e%5E%7B1.6t%7Ddt%5C%5CP%28t%29%3D%5Cfrac%7B4.058%7D%7B1.6%7D%20%28e%5E%7B1.6t%7D%20%2BK%29%5C%5CP%28t%29%3D2.53625%20%28e%5E%7B1.6t%7D%20%2BK%29)
Where k is a constant of Integration.
At t=0, P(t)=36
![36=2.53625 (e^{1.6*0} +K)\\36=2.53625 (e^{0} +K)\\36=2.53625 (1 +K)\\36=2.53625 +2.53625K\\K=13.19](https://tex.z-dn.net/?f=36%3D2.53625%20%28e%5E%7B1.6%2A0%7D%20%2BK%29%5C%5C36%3D2.53625%20%28e%5E%7B0%7D%20%2BK%29%5C%5C36%3D2.53625%20%281%20%2BK%29%5C%5C36%3D2.53625%20%2B2.53625K%5C%5CK%3D13.19)
Therefore:
![P(t)=2.53625 (e^{1.6t} +13.19)\\At \: t=4\\P(4)=2.53625 (e^{1.6*4} +13.19)\\=1559.88\\P(4)=1560](https://tex.z-dn.net/?f=P%28t%29%3D2.53625%20%28e%5E%7B1.6t%7D%20%2B13.19%29%5C%5CAt%20%5C%3A%20t%3D4%5C%5CP%284%29%3D2.53625%20%28e%5E%7B1.6%2A4%7D%20%2B13.19%29%5C%5C%3D1559.88%5C%5CP%284%29%3D1560)