Rosario is an ecologist who studies the change in the penguin population of Antarctica over time. The relationship between the elapsed time ttt, in years, since Rosario started studying the population, and the number of penguins, P(t)P(t)P, left parenthesis, t, right parenthesis, is modeled by the following function:

P(t) = 21,00(4/7)^(t/3)

Complete the following sentence about the rate of change in the penguin population.
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The population of penguins loses 3/7 of its size every _ years.

Eliza wants to make $10,000 from her investments. she finds an investment account that earns 4.5% interest. she decides to deposit $2,500 into an account. how much money will be in her account after 14 years?

Which of the following is the maximum value of the equation y=-x^2+2x+5 a. 5 b. 6 c. 2. d. 1

I've been working on this for a few days and i just don't understand, it's due in a few hours. you.the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α.part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part bsuppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i.e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case.part cnow try a numerical problem. what is the direction of the vector w = < -1, 6 > ?