Determine whether the function represents exponential growth or $$ y=(1.06)^{8 t} $$ Exponential growth Expontial decay The rate of change is 6 Listen

Question

UpStudy AI · Accepted Answer

To determine whether the function $$ y = (1.06)^{8t} $$ represents exponential growth or decay, we need to analyze the base of the exponent. 1. **Identify the base**: In the function $$ y = (1.06)^{8t} $$, the base is $$ 1.06 $$. 2. **Determine growth or decay**: - If the base is greater than 1 (i.e., $$ b > 1 $$), the function represents exponential growth. - If the base is between 0 and 1 (i.e., $$ 0 < b < 1 $$), the function represents exponential decay. Since $$ 1.06 > 1 $$, we can conclude that the function represents **exponential growth**. 3. **Rate of change**: The rate of change in this context refers to the growth factor. The growth factor is $$ 1.06 $$, which indicates a growth rate of $$ 6\% $$ per unit of $$ t $$. Thus, the final conclusion is: - The function $$ y = (1.06)^{8t} $$ represents **exponential growth** with a growth rate of $$ 6\% $$. The function $$ y = (1.06)^{8t} $$ represents **exponential growth** with a growth rate of $$ 6\% $$.

Determine whether the function represents exponential growth or \( y=(1.06)^{8 t} \) Exponential growth Expontial decay The rate of change is 6 Listen

Real Tutor Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Pre Algebra Questions