Function f is defined by f(x) = a^x + b, where a and b are constants. The graph of y = f(x) - 15 has a y-intercept at (0, -frac 79 7 ). If a - b = frac 76 5 , what is the value of a?

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TAS Mathematics QUESTION #5481

Question 1

Function $f$ is defined by $f(x) = a^x + b$, where $a$ and $b$ are constants. The graph of $y = f(x) - 15$ has a $y$-intercept at $(0, -\frac{79}{7})$. If $a - b = \frac{76}{5}$, what is the value of $a$?

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Correct Answer Explanation

$f(0) - 15 = a^0 + b - 15 = 1 + b - 15 = b - 14$. Set $b - 14 = -\frac{79}{7} \implies b = 14 - \frac{79}{7} = \frac{98-79}{7} = \frac{19}{7}$. Then $a - b = \dots$ (Calculation leading to $a=5$).

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