Question

MATH QUESTION HELP PLEASE

Does each equation represent exponential decay or exponential growth?
Drag and drop the choices into the boxes to correctly complete the table.
Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.
Exponential Decay Exponential Growth

options:
H=5.9 (0.82)^t
y=0.8 (3.6)^t
f(t)=0.72 (15)^t
A=4/9 (8)^t
A= (4/3)^t
H= 7/2 (5/6)^t
g(x)= 0.3(x)

Answer 1

Whenever number less than 1 is raised to the power of "t" , the equation is exponentially decaying.
This is because as time increases the decimal is being raised to a higher and higher power causing it to decay. For example, when
t= 0 sec in eq 1 the H= 5.9(0.82)^0 = 5.9(1). So, at time= 0 seconds H= 5.9.
but, if time increases to t=2secs, then H= 5.9(0.82)²= (5.9)(0.6724)= 3.96716.
At time = 2 seconds H= 3.96716.

In the other case, where a value greater than 1 is raised to the power of time(t) the equation is an exponential growth equation.

ANSWER:
Exponential Decay:
H= 5.9(0.82)^t
A= (3/4)^t
H= 7/2(5/6)^t
Exponential Growth:
y=0.8(3.6)^t
f(t)= 0.72(15)^t
A= 4/9 (8)^t

Niether:
g(x)= 0.3x - Neither growth nor decay because nothing in the equation is being raised to an exponential power of "t" (time)