Question
7) Here is a graph that represents \( f(x)=5 \cdot 2^{x} \). The coordinates of \( A \) are \( (1, c) \) and the coordinates of \( B \) are \( (4, d) \). What is the value of \( \frac{d}{c} \) ? Show or explain your reasoning.
Ask by Wright Cervantes. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{d}{c} = 8 \)
Solution
We are given the function f(x) = 5 · 2^x.
For point A at x = 1:
c = f(1) = 5 · 2^1 = 10.
For point B at x = 4:
d = f(4) = 5 · 2^4 = 80.
Thus, the ratio d/c is:
80 / 10 = 8.
Alternatively, notice that increasing the x value from 1 to 4 multiplies the function's value by 2^(4-1) = 2³ = 8, so d/c = 8.
The answer is 8.
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Simplify this solution Mind Expander
To find the values of \( c \) and \( d \) from the function \( f(x) = 5 \cdot 2^{x} \), we can substitute the \( x \)-coordinates of points \( A \) and \( B \). For point \( A \) where \( x = 1 \): \[ c = f(1) = 5 \cdot 2^{1} = 5 \cdot 2 = 10. \] For point \( B \) where \( x = 4 \): \[ d = f(4) = 5 \cdot 2^{4} = 5 \cdot 16 = 80. \] Now we can calculate \( \frac{d}{c} \): \[ \frac{d}{c} = \frac{80}{10} = 8. \] So, the value of \( \frac{d}{c} \) is \( 8 \).
