NO CLUE how TO DO THIS PROBLEM

EXPLANATION AND ANSWERS?
WE RECENTLY LEARNED TO DO Y=km^x+b IF THAT HELPS!

You are a mathematician for a major movie company. You are figuring projected sales for their newest movie, which is currently being filmed. You find that as filming starts 1.6 million dollars have already been spent and that after two months 5.4 million have been spent. Assume that the cost of the movie varies exponentially with the number of months it takes to film it.

A. Define the variables and write the particular equation.

B. The movie takes a total of 5 months to film. How much will it cost?

C. Use you model to predict the cost of Semmens vs. Smith Part XXI, which took 1 year to film.

D. The movie the Pirates of the swamp, the curse of Winkel and Arthofer cost 25 million to film. How long did it take to film?

Y(cost, in millions) = k * m^x

(x = # of months)
Since Y = 1.6 at t = 0,
1.6 = k
Since Y = 5.4 at t = 2,
5.4 = k*m^2
m^2 = 3.375
m = 1.837

Y = 1.6 *1.837^x

If x = 5, Y = 33.5 million

x=12, Y = 2362 million

A. Variables:

- Y represents the cost of the movie in millions of dollars.
- x represents the number of months it takes to film the movie.

Let's use the given information to determine the equation for the cost of the movie.

We know that at the start of filming, 1.6 million dollars have already been spent. So, when x = 0, Y = 1.6.

We also know that after two months, 5.4 million dollars have been spent. So, when x = 2, Y = 5.4.

Since the cost of the movie varies exponentially with the number of months, we can use the equation Y = km^x + b.

Let's substitute the known values into the equation and solve for k and b.

When x = 0:
1.6 = km^0 + b
1.6 = k + b (since any number raised to the power of 0 is 1)

When x = 2:
5.4 = km^2 + b

Now we have two equations with two unknowns (k and b). We can solve this system of equations to find the values of k and b.

B. To find the cost of the movie when it takes 5 months to film, we substitute x = 5 into the equation Y = km^x + b

C. To predict the cost of Semmens vs. Smith Part XXI, which took 1 year (12 months) to film, we substitute x = 12 into the equation Y = km^x + b.

D. To find out how long it took to film "The Pirates of the Swamp, The Curse of Winkel and Arthofer" which cost 25 million to film, we need to solve the equation 25 = km^x + b for x.