a. Determine whether the function y = 2(0.82)' represents exponential growth or exponential decay. The function represents exponential b. Identify the percent rate of change of the function in part (a). The rate of change is %.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Exponential Functions
#### Problem Statement
Consider the following function:
\[ y = 2(0.82)^t \]
a. **Determine whether the function represents exponential growth or exponential decay.**
*The function represents exponential (growth/decay).*
b. **Identify the percent rate of change of the function in part (a).**
*The rate of change is* \[ \boxed{\ } \% \].
#### Explanation
In part (a), to determine whether the given function \( y = 2(0.82)^t \) represents exponential growth or decay, observe the base of the exponential, which in this case is 0.82. If the base is less than 1, the function represents exponential decay. If the base is greater than 1, it represents exponential growth.
In part (b), the percent rate of change can be calculated by subtracting the base of the exponential (in decimal form) from 1 and then expressing the result as a percentage. If the base is a number \( b \) such that \( 0 < b < 1 \), then the rate of decay is \((1 - b) \times 100\%\). If \( b > 1 \), then the rate of growth is \((b - 1) \times 100\%\).
For instance, in this problem, since the base is 0.82, the function represents exponential decay. The rate of decay can be calculated as \((1 - 0.82) \times 100\% = 18\%\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a18a320-2046-4089-b27e-0ca38db1d2b2%2F82cd709b-2e8b-47dc-bfe4-a4aa657c4fd3%2Famfg8zq.jpeg&w=3840&q=75)
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