Question

Does each equation represent exponential decay or exponential growth?

Answer 1

Answer:

The best way to know if an equation represents an exponential growth or decay is to look a the base of the exponentiation.

If the base is larger than 1, it will be an exponential growth.

For example, $3^{2} = 9$

If the base is smaller than 1, it will be an exponential decay.

For example, $0.5^{2} = 0.25$

If the function does not have an exponent, that means there will be no exponential growth or decay.

Therefore:

Exponential Decay (base smaller than 1):

$W=\frac{9}{8}(\frac{3}{5})^{t}$

$f(t)=(\frac{3}{4}) ^t$

$L=4.2(0.6)^t$

Exponential Growth (base larger than 1):

$L=0.25(12)^t$

$W=0.5(2.1)^t$

$f(t)=2/3(6)^t$

Not exponential growth or decay (no exponent):

G(x)=1.3(x)

Answer 2

Exponential Decay:

W=9/8(3/5)^t

f(t)=(3/4)^t

L=4.2(0.6)^t

Exponential Growth:

L=0.25(12)^t

W=0.5(2.1)^t

f(t)=2/3(6)^t

Neither:

G(x)=1.3(x)