Question

Does each equation represent exponential decay or exponential growth?

Answer 1

Answer:

$H=5.9 (0.82)^t$ -- Exponential decay

$y=0.8 (3.6)^t$ -- Exponential growth

$f(t)=0.72 (15)^t$ -- Exponential growth

$A=4/9 (8)^t$ -- -- Exponential growth

$A= (4/3)^t$ -- -- Exponential growth

$H= 7/2 (5/6)^t$ -- Exponential decay

Step-by-step explanation:

The equations are:

$H=5.9 (0.82)^t$

$y=0.8 (3.6)^t$

$f(t)=0.72 (15)^t$

$A=4/9 (8)^t$

$A= (4/3)^t$

$H= 7/2 (5/6)^t$

An exponential equation is of the form

$y = ab^x$

Where

$b = rate$

If $b > 1$, then it is a growth

If $b < 1$, then it is a decay

If $b = 1$, then it is none.

Analyzing each equation

1.

$H=5.9 (0.82)^t$

By comparison with $y = ab^x$

$b = 0.82$

$0.82 < 1$

So:

$H=5.9 (0.82)^t$ represents an exponential decay

2.

$y=0.8 (3.6)^t$

By comparison with $y = ab^x$

$b = 3.6$

$3.6 > 1$

So:

$y=0.8 (3.6)^t$ represents an exponential growth

3.

$f(t)=0.72 (15)^t$

By comparison with $y = ab^x$

$b = 15$

$15>1$

So:

$f(t)=0.72 (15)^t$ represents an exponential growth

4.

$A=4/9 (8)^t$

By comparison with $y = ab^x$

$b = 8$

$8>1$

So:

$A=4/9 (8)^t$ represents an exponential growth

5.

$A= (4/3)^t$

By comparison with $y = ab^x$

$b = 4/3$

$b = 1.33$

$1.33>1$

So:

$A= (4/3)^t$ represents an exponential growth

6.

$H= 7/2 (5/6)^t$

By comparison with $y = ab^x$

$b=5/6$

$b = 0.83$

$0.83$

So:

$H= 7/2 (5/6)^t$ represents an exponential decay