This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Sawa A, hebu tushughulikie swali la 10. Step 1: Tambua fomula ya ukuaji wa bakteria na maadili yaliyotolewa. Fomula ni P(t) = P_0 e^rt. Tunaambiwa: • Idadi ya awali (P_0) = 200 • Idadi huongezeka mara mbili katika masaa 5. Hii inamaanisha kuwa P(5) = 2 × P_0 = 2 × 200 = 400 wakati t = 5 masaa. Step 2: Ingiza maadili haya kwenye fomula. Tunajua P(5) = 400, P_0 = 200, na t = 5. 400 = 200 e^r × 5 Step 3: Rahisisha mlinganyo ili kutafuta r. Gawanya pande zote mbili kwa 200: (400)/(200) = e^5r 2 = e^5r Step 4: Tumia logarithm asilia (ln) kuondoa e. Chukua ln ya pande zote mbili: (2) = (e^5r) Kutokana na sheria za logarithm, (e^x) = x: (2) = 5r Step 5: Tatua kwa r. Gawanya pande zote mbili kwa 5: r = ((2))/(5) Tumia kikokotoo kupata thamani ya (2) ≈ 0.6931: r = (0.6931)/(5) r ≈ 0.13862 Kiwango cha ukuaji r ni takriban 0.1386 (kwa sehemu nne za desimali). P(t) = P_0 e^rt 400 = 200 e^r × 5 2 = e^5r (2) = 5r r = ((2))/(5) r ≈ (0.693147)/(5) r ≈ 0.138629 Kiwango cha ukuaji r ni 0.1386. That's 2 down. 3 left today — send the next one.