Asap.
1. a marine biologist is studying the growth of a particular species of fish. she writes the following equation to show the length of the fish, f(m), in cm, after m months:

f(m) = 4(1.08)m

part a: when the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. what is a reasonable domain to plot the growth function? (4 points)

part b: what does the y-intercept of the graph of the function f(m) represent? (2 points)

part c: what is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent? (4 points)

2.
the price of fuel may increase due to demand and decrease due to overproduction. marco is studying the change in the price of two types of fuel, a and b, over time.

the price f(x), in dollars, of fuel a after x months is represented by the function below:

f(x) = 2.96(1.04)x

part a: is the price of fuel a increasing or decreasing and by what percentage per month? justify your answer. (5 points)

part b: the table below shows the price g(m), in dollars, of fuel b after m months:

m (number of months) 1 2 3 4
g(m) (price in dollars) 3.04 3.22 3.41 3.61

which type of fuel recorded a greater percentage change in price over the previous month? justify your answer. (5 points)

3.
belinda is thinking about buying a house for $249,000. the table below shows the projected value of two different houses for three years:

number of years 1 2 3
house 1 (value in dollars) 253,980 259,059.60 264,240.79
house 2 (value in dollars) 256,000 263,000 270,000

part a: what type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? explain your answer. (2 points)

part b: write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)

part c: belinda wants to purchase a house that would have the greatest value in 45 years. will there be any significant difference in the value of either house after 45 years? explain your answer, and show the value of each house after 45 years. (4 points)

4.
aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. to prepare for the event, she is practicing and keeping track of her time to complete each station.

the x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 4), (2, 8), (3, 16), (4, 32)

part a: is this data modeling an algebraic sequence or a geometric sequence? explain your answer. (2 points)

part b: use a recursive formula to determine the time she will complete station 5. show your work. (4 points)

part c: use an explicit formula to find the time she will complete the 8th station. show your work. (4 points)