f(x) Function f is defined by = −a^x + b, where a and b are constants. In the xy-plane, the graph of ⎛ ⎞ f(x) ⎜ ⎟ y = − 15 has a y-intercept at ⎜ 0, − ⎟. The ⎝ 99/7 ⎠⎟ product of a and b is 65/7. What is the value of a?
","rationale_html":"( =) - x+ - x+ The correct answer is 5. It’s given that f x a b. Substituting a b for ( ) (=) - =- +x - f x in the equation y f x 15 yields y a b 15. It’s given that the (=) - ( -99 ) y-intercept of the graph of y f x 15 is 0, . Substituting 0 for x and 7 -99 =- +x - -99=- 0+ - for y in the equation y a b 15 yields a b15, which is 7 7 -99=- + - -99 = - equivalent to 1 b 15, or b 16. Adding 16 to both sides of this 7 7 13= 65 =65 equation yields b. It’s given that the product of a and b is , or ab . 13 7 ( )( 13 ) =65 7 7 Substituting for b in this equation yields a . Dividing both sides of 7 7 7 13 = this equation by yields a 5. 7 43 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS
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