Solve the initial value problem: y= 0.05y + 5 y(0) = 100 y(t) =

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.

Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.

Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.

When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?

Solve for y: x = 4ln(y - 8). 1 4 ln(x - 8) Oy= Oy = x + 8 4 O y = e-4x + 8 O y = 4 ln(x - 8) Oy = ex/4 + 8

If the growth rate of the number of bacteria at any time (t) is proportional to the number present at (t) and doubles in 1 week, how many bacteria can be expected after 18 days if the initial amount is 1000?

Find the half-life of radioactive substance Radium-226; A(t) = A0e-0.00043t

Given the rate of change of a quantity Q and its initial value Q(0), explain how to find the value of Q at a future time t ≥ 0.

Find the consumers surplus and producers surplus for p= D(x)= 71- 1/10x and p=S(x)=35+1/20x