Question

Exponential growth and decay functions are written in standard form F (t)= A_0•b^kt, where A_0 is an initial amount, b is the growth factor, k is the growth rate, and t is

Answer 1

t is the time elapsed since the concentration was the A_=, this is the initial concentration.

For example, for A_0 = 250, k = -10 (it has to be negative because this is a decay function) and b = 24, the function will be:

F(t) = 250 *  24 ^ (- 10 t)

And so, given that t is the time, you have the relation that gives the value of the dependent variable as a function of the time t. If the unit is hours, you could make this table:

time, t in hours             F(t) = 250 * 24 ^ ( -10t)

0                                   250 * 24 ^(0) = 250

0.01                              250 * 24 ^ (- 10 * 0.01) ≈ 0.73

0.1                                250 * 24 ^ (-10* 0.1) ≈ 0.042

1                                  250 * 24 ^ ( -10) ≈ 0.000000000000016

Answer 2

Answer: Hello mate!

Exponential growth and decay functions are written as:

F(t) = A₀b^(kt)

We know that A₀ is the initial amount (at the time equal to zero)

b is the growth factor, k is the growth rate, and t is the time (the independent variable)

Note that b is a real and positive number, while A₀ and k can be also negative.

If k is a positive number, then as time grows, the product k*t also increases, and then the factor b^(kt) also increases, and now you have exponential growth.

if k is a negative number, you have the inverse situation, you have an exponential decay.