Question

Tell if each equation represents exponential growth, exponential decay or neither.

a. f(t)=2/5 (7/3)^t
b. P=22(1.76)^x
c. V=1/3 (0.45)^x
d. W=3.2(x)
e. g(x)=4.2(1/3)^x

Answer 1

A_Exponential growth

B_Exponential growth

C_exponential decay

D_ neither

E_exponential decay

Explanation:

Answer 2

Exponential growth A, B;

exponential decay C, E;

neither D.

Explanation:

The function
`y=a\cdot b^x`

• represents exponential growth when
  `b>1;`
• represents exponential decay when
  `0<b<1.`

A. The equation
`f(t)=(2)/(3)\cdot \left((7)/(3)\right)^t` represents exponential growth, because
`(7)/(3)>1.`

B. The equation
`P=22\cdot \left(1.76\right)^x` represents exponential growth, because
`1.76>1.`

C. The equation
`V=(1)/(3)\cdot \left(0.45\right)^x` represents exponential decay, because
`0<0.45<1.`

D. The equation
`W=3.2\cdot (x)` represents neither exponential growth nor exponential decay, because this function is linear.

E. The equation
`g(x)=4.2\cdot \left((1)/(3)\right)^x` represents exponential decay, because
`0<(1)/(3)<1.`