Solve the following IVP: (7et '+ 9y = {o if 0 5 y'(0) = -1. %3D y(0) = 0, Note: Write your final answer in terms of UNIT STEP FUNCTION and your six constants. DON’T SOLVE FOR THE CONSTANTS.

The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by  y = 285 − 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time. (i) 0.1 seconds  (ii)0.05 seconds  (iii)0.01 seconds  (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.

PA = (9t7 ve that 02X 2 X 46) 0>X 90

Because of the rainy season, the depth in a pond increases 3% each week. Before the rainy season started, the pond was 10 feet deep. What is the equation that best represents the depth of the pond each week? Hint: Use the formula y=P(1+r)^(x)