A seismologist analyzing earthquake data observes that the amplitude of seismic waves increases exponentially by 15% every 2 seconds. If the initial amplitude is 40 units, what will the amplitude be after 10 seconds?

["Understanding Exponential Growth in Earthquake Seismic Waves", "Seismologists study seismic wave behavior to understand earthquake dynamics, and one key insight is how wave amplitude evolves over time. In this article, we explore a real-world example of exponential growth in seismic amplitude—an essential concept for analyzing earthquake intensity and potential impacts.", "According to recent data analyzed by seismologists, the amplitude of seismic waves increases by 15% every 2 seconds. Starting with an initial amplitude of 40 units, scientists model this change using exponential growth. The growth follows the formula:", "[ A(t) = A_0 \ imes (1 + r)^{t/T} ]\nWhere:\n- ( A(t) ) = amplitude at time ( t )\n- ( A_0 ) = initial amplitude (40 units)\n- ( r ) = growth rate per 2-second interval (15% = 0.15)\n- ( T ) = time interval (2 seconds)\n- ( t ) = total time in seconds", "We want to find the amplitude after 10 seconds. Since the growth occurs every 2 seconds, there are ( \frac{10}{2} = 5 ) intervals. Applying the formula:", "[ A(10) = 40 \ imes (1 + 0.15)^5 ]\n[ A(10) = 40 \ imes (1.15)^5 ]", "Calculating ( 1.15^5 ):\n( 1.15^5 \approx 2.011357 )", "Thus,\n[ A(10) \approx 40 \ imes 2.011357 = 80.454 ] units", "Therefore, after 10 seconds, the seismic wave amplitude reaches approximately 80.45 units.", "This exponential increase highlights how even moderate increases in amplitude grow rapidly, emphasizing the importance of real-time monitoring and preparedness in seismology. Understanding these patterns helps scientists better predict earthquake effects and improve early warning systems.", "For anyone analyzing seismic data, recognizing such exponential trends enables more accurate modeling and timely alerts—critical for saving lives in earthquake-prone regions."]