If f(a) is an exponential function where f(-3) = 18 and f(1) = 59, then find the value of f(0), to the nearest hundredth.

Given:

For en exponential function f(a):

To find:

The value of f(0).

Solution:

The general form of an exponential function is:

         ...(i)

Where, a is the initial value and b is the growth/ decay factor.

We have, . Substitute in (i).

           ...(ii)

We have, . Substitute in (i).

           ...(iii)

On dividing (iii) by (ii), we get

Substituting the value of b in (iii).

The initial value of the function is 43.83. It means, .

Therefore, the value of f(0) is 43.83.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.