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`1.01^365=37.8` , `0.99^365=0.03` |
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Answer» (i) Let `t = 1.01^365` `:. log_10t = 365log_10(1.01)` `=> log_10t = 365(log_10(101) - log_10(100))` `=> log_10t = 365(2.00432 - 2)`.... (As `log_10(101) = 2.00432`) `=> log_10t = 365(.00432)` `=> log_10t = 1.5773` `=> t = 10^(1.57773)` `=> t = 37.78` `:. 1.01^365 = 37.78` (ii)Let `z = 0.99^365` `:. log_10z = 365log_10(0.99)` `=> log_10z = 365(log_10(99) - log_10(100))` `=> log_10z = 365(1.9956 - 2)`....(As `log_10(99) = 1.9956`) `=> log_10z = 365(-.0044)` `=> log_10z = -1.606` `=> z = 10^(-1.606)` `=> z = 0.025` `:. 0.99^365 = 0.025 ~= 0.03 ` |
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