# Thread: Logs & Functions Integral

1. ## Logs & Functions Integral

Hey so I have this question dealing with logarithms and exponential functions. Can anyone shed some light on it?

edit for clarity:

The question is essentially there are 2 cars. You are Car A and you want to race Car B. You need to meet 3 out of 4 of the requirements in order to successfully win. You need to determine the 4 questions for each equation ( Both car A and car B)
2 cars, each has their own formula.

A- V(t)= 19.74 x 3 ^ (1975t-1) (Max velocity of your car is 450 km/h)
B- P(t)= -344990 log (-0.5(t-2))

The questions:

1- Car A 0-100km/h faster than Car B?
2- Car A's Max velocity before 6.5 seconds greater than Car B?
3- Car A has Higher average rate of acceleration over first 8 seconds than Car B?
4- Car A's Instanteous rate of acceleration greater than Car B at 5 seconds

Thanks for the help!

2. Originally Posted by fuzy
Hey so I have this question dealing with logarithms and exponential functions. Can anyone shed some light on it?

edit for clarity:

The question is essentially there are 2 cars. You are Car A and you want to race Car B. You need to meet 3 out of 4 of the requirements in order to successfully win. You need to determine the 4 questions for each equation ( Both car A and car B)
2 cars, each has their own formula.

A- V(t)= 19.74 x 3 ^ (1975t-1) (Max velocity of your car is 450 km/h)
B- P(t)= -344990 log (-0.5(t-2))

The questions:

1- Car A 0-100km/h faster than Car B?
2- Car A's Max velocity before 6.5 seconds greater than Car B?
3- Car A has Higher average rate of acceleration over first 8 seconds than Car B?
4- Car A's Instanteous rate of acceleration greater than Car B at 5 seconds

Thanks for the help!
There has got to be something messed up in the formula for car A. The maximum velocity is far far higher than 450 km/h. My calculator can barely manage calculating V(1), much less than for any time larger than that!

I don't understand what question 1 is asking for.

2. To find a maximum velocity you need to solve
$\frac{dv}{dt} = 0$
for t and show that you have a maximum at that t.

3. Do they really mean average acceleration or rate of acceleration I wonder? By the mean value theorem, the average rate of acceleration is
$\bar{\frac{da}{dt}} = \frac{1}{8 - 1} \int_0^8 \frac{da}{dt}~dt$
(By the way, the time rate of change of acceleration is called a "jerk.")

4. The instantaneous rate of acceleration is da/dt.

-Dan