Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 2ECP: The number of bacteria in a culture is increasing according to the law of exponential growth. After...
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The answer for b is fractions are not accepted
![**Solving Exponential Functions**
An exponential function is given by the equation \( f(x) = ab^x \) and it passes through the points (0, 9000) and (2, 2250). We need to determine the values of \( a \) and \( b \).
Given points:
- \( (0, 9000) \)
- \( (2, 2250) \)
From the point (0, 9000):
\[ f(0) = ab^0 = a = 9000 \]
To find \( b \), we use the point (2, 2250) and the value of \( a \) we just found:
\[ f(2) = ab^2 = 9000b^2 = 2250 \]
\[ b^2 = \frac{2250}{9000} \]
\[ b^2 = \frac{1}{4} \]
\[ b = \frac{1}{2} \]
Thus, the values are:
- \( a = 9000 \) (correctly indicated by the tick mark)
- \( b = \frac{1}{2} \) (incorrectly indicated by the cross mark, but this is actually correct mathematically)
This explanation solves for the values of \( a \) and \( b \) in the exponential function \( f(x) = ab^x \). The color-coded tick and cross marks indicate interactive feedback on whether the correct values were chosen.
For further detail or any queries, feel free to contact us through our educational platform's support section.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7167f26-c4aa-4cbc-ab2c-28c429d612af%2Fe7d5f522-926e-445d-80a5-bfcb31c9ce0e%2Fk7ijw6m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Exponential Functions**
An exponential function is given by the equation \( f(x) = ab^x \) and it passes through the points (0, 9000) and (2, 2250). We need to determine the values of \( a \) and \( b \).
Given points:
- \( (0, 9000) \)
- \( (2, 2250) \)
From the point (0, 9000):
\[ f(0) = ab^0 = a = 9000 \]
To find \( b \), we use the point (2, 2250) and the value of \( a \) we just found:
\[ f(2) = ab^2 = 9000b^2 = 2250 \]
\[ b^2 = \frac{2250}{9000} \]
\[ b^2 = \frac{1}{4} \]
\[ b = \frac{1}{2} \]
Thus, the values are:
- \( a = 9000 \) (correctly indicated by the tick mark)
- \( b = \frac{1}{2} \) (incorrectly indicated by the cross mark, but this is actually correct mathematically)
This explanation solves for the values of \( a \) and \( b \) in the exponential function \( f(x) = ab^x \). The color-coded tick and cross marks indicate interactive feedback on whether the correct values were chosen.
For further detail or any queries, feel free to contact us through our educational platform's support section.
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