Talulah is an ecologist who studies the change in the penguin population of Antarctica over time. She

observed that the population decays by a factor of every 4 months. The population of penguins can be

modeled by a function, P. which depends on the amount of time, t (in months)

When Talulah began the study, she observed that there were 27,000 penguins in Antarctica.

Write a function that models the population of the penguins t months since the beginning of Talulah's

P(t) =

What is an alternate exterior angle

X/y + 4y/x divided by x/y - 2y/x explain as in depth as you can how you simplfied the fractions. i don't know where to start on this : /

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?