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.
for example: f(x)=3*2^x write the thing and look at the picture asap ty
![### Problem Statement
Write an exponential function that contains the points \( (3,32) \) and \( (6,256) \).
### Solution
To find the exponential function that passes through the given points, we start with the general form of an exponential function:
\[ y = ab^x \]
Using the given points, we can set up a system of equations. For the point \( (3, 32) \):
\[ 32 = ab^3 \]
For the point \( (6, 256) \):
\[ 256 = ab^6 \]
By dividing the second equation by the first, we eliminate \(a\) and solve for \(b\):
\[ \frac{256}{32} = \frac{ab^6}{ab^3} \]
\[ 8 = b^3 \]
Taking the cube root of both sides:
\[ b = \sqrt[3]{8} \]
\[ b = 2 \]
Now that we have \( b \), we can substitute it back into the first equation to solve for \(a\):
\[ 32 = a(2)^3 \]
\[ 32 = a \cdot 8 \]
\[ a = \frac{32}{8} \]
\[ a = 4 \]
Thus, the exponential function that contains the points \( (3, 32) \) and \( (6, 256) \) is:
\[ y = 4 \cdot 2^x \]
### Verification
To ensure our solution is correct, let's verify the function with the given points:
- For \( (3, 32) \):
\[ y = 4 \cdot 2^3 = 4 \cdot 8 = 32 \]
- For \( (6, 256) \):
\[ y = 4 \cdot 2^6 = 4 \cdot 64 = 256 \]
Both points satisfy the equation, confirming that the derived exponential function \( y = 4 \cdot 2^x \) is accurate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F541e9811-c8f1-44f7-9808-3fa399aa819f%2Fd1314776-1983-48d9-97af-da8557fd2d63%2Fgsiyyyd_processed.png&w=3840&q=75)
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