What is Exponential growth/ or decay?
Exponential growth and decay apply to quantities that change rapidly. Exponential growth and decay have been derived from the concept of geometric progression. Quantities that do not change as constant but a change in an exponential manner can be termed as having exponential growth or exponential decay. The simplest representation of exponential growth and decay is the formula abx, where 'a' is the initial quantity, 'b' is the growth factor which is similar to the common ratio of the geometric progression, and 'x' is the time steps for multiplying the growth factor. For exponential growth, the value of b is greater than 1 (b > 1), and for exponential decay, the value of b is lesser than 1 (b < 1). Exponential growth finds applications in studying bacterial growth, population increase, and money growth schemes. Exponential decay refers to a rapid decrease in a quantity over a period of time. The exponential decay can be used to find food decay, half-life, and radioactive decay. The formula of exponential growth and decay is presented below:
x(t)= x0 × (1 + r) t
x(t)= the value at time t.
x0= the initial value at time t=0.
r= the growth rate when r>0 or the decay rate when r<0, in percent.
t= the time in discrete intervals and selected time units.
Substitute values into the formula (R>12%)
34×(1+12%)10=
105.5988390837
Rounding
Now since there is no possible way that there can be 105.5988390837 whales we gotta round it up
9>5 (we will round it up to 105.6)
6>5 (The 6 rounds up to 106)
So there will be about 106 whales in 12 years if going the annual rate of 12%