2. Determine the rule of an exponential function that has the given properties. Validate your answer using a graph. (4 ch) a. Has a base of 6, an asymptote at y=-7, has parameter k = ±1, and passes through the coordinate points (3,-4) and (4, 11). b. Has an initial value of 4893, passes through the coordinate point (-2, 93) and has a range of {yly> -7, y R}. c. Has a range of {yly < 0, y R}, has a base of 2, has no horizontal translation from the base function, and passes through the coordinate points (0, -37.6) and (7, -75.2).

Write a CNC G-code program to machine the part in the following figure, so that the tip of the tool follows this path: rapid movement to a point above P8, with z=4 . using absolute dimensioning change to tool "4, with a clockwise spindle speed of 2500 rpm, with coolant on and a feed rate of 14 in./min using incremental dimensioning -rapid movement to 4 in. above P1 -rapid movement to lower the tool to be 0.1 in. above the top surface of the part -move the tool to be 0.5 in. below the top at a 14 in./min feed rate -follow the path around the perimeter to points P2 through PI, ending at P1, using the 14in„/min feed rate turn off the spindle and coolant use absolute dimensioning to return to the start point end the program

The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.

The number N of beavers in a given area after x years can be approximated by N=5.5100.23x,0x10. Use the model to approximate how many years it will take for the beaver population to reach 78.

If you travel 300 miles on the first day and then drive v miles per hour for t hours on the second day, then the total distance traveled over the teo-day period is given by d=300+vt miles. Use a formula to express v as a function of d and t for this two-day event.

Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?