Spread of a Rumor A rumor spreads through a small town. Let be the fraction of the population that has heard the rumor at time and assume that the rate at which the rumor spreads is proportional to the product of the fraction of the population that has heard the rumor and the fraction that has not yet heard the rumor. Write the differential equation satisfied by in terms of a proportionality factor Find (in units of ), assuming that 10% of the population knows the rumor at and 40% knows it at days. Using the assumptions of part (b), determine when 75% of the population will know the rumor.

answer: no, but if it does it's a obvious pattern.

step-by-step explanation:

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places