Question

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

Answer 1

Answer:

Exponential growth A, B;

exponential decay C, E;

neither D.

Step-by-step explanation:

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

• represents exponential growth when $b>1;$
• represents exponential decay when $0$

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

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

C. The equation $V=\dfrac{1}{3}\cdot \left(0.45\right)^x$ represents exponential decay, because $0$

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

E. The equation $g(x)=4.2\cdot \left(\dfrac{1}{3}\right)^x$ represents exponential decay, because $0$