Chapter 6 - Section 6.8 - Exponential Growth and Decay Models; Newton's Law: Logistic Growth and Decay Models - 6.8 Assess Your Understanding - Page 486: 6

See below.

a) $N(t)=N_0e^{kt}$ b) We know that $800=500e^{k\cdot1}\\1.6=e^k\\k=\ln1.6\approx0.47000362925$ Thus $N(5)=500e^{0.47000362925\cdot5}=5243$ c) Our equation is: $20000=500e^{0.47000362925\cdot t}\\40=e^{0.47000362925\cdot t}\\\ln{40}=0.47000362925\cdot t\\t=\frac{\ln{40}}{0.47000362925}\approx7.85$