The Exponential Function and Its Inverse

Hi I got 3 questions that I am stuck on in my homework. Any help explaining how you came across the answer would help. Thanks in advance.

1. The probability, *P* percent, of having an accident while driving a a car is related to the alcohol level of the driver's blood by the formula P= *e*^(*kt)*, where *k * is the constant. Accident statistics show that the probability of an accident is 25% when the blood alcohol level is *t* = 0.15.

a) Find *k. *Use P=25

b) At what blood alcohol level is the probability of having an accident 50 %.

2. A failure of o-ring seals caused the challenger space shuttle disaster in 1986. After the disaster, there was a study of 23 shuttle launches that had preceded the fatal flight. A mathematical model was developed involving the relationship between the Celsius temperature, x, around the o-rings and the number, y, of eroded of leaky primary o-rings. The model sated that y = ( 6) / (1 + e^[-{5.085-0.1146x}]), where the number 6 indicates the 6 primary o-rings on the spacecraft.

a) What is the predicted number of eroded or leaky primary o-rings at a temperature of 37.5 degrees Celsius.