Chapter 4 - Exponential Functions - 4.3 Graphs of Exponential Functions - Exercises and Problems for Section 4.3 - Exercises and Problems - Page 163: 37

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As $r$ increases, the graph of $y=a(1+r)^t$ rises steeply, so the point of intersection moves to the left and down. However, no matter how steep the graph becomes, the point of intersection remains above and to the right of the $y$-intercept of the second curve, or the point $(0, b)$. Hence, the value of $y_0$ decreases but does not reach $b$.