Auczyt Com
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Solntion
a) The amount at the end of each year forms a GP, 0,01,
The first term, a=¢100000 and the common ratio, r= 1.08
Hence the second term is a=(100 000(1.08)=4108 000, which is the valne after 1 year
The third term is ar? =(100 000)(L08)2 = $116 640 which is the valve after 2 years,
and so on.
Therefore the value after 10 years='=(100 000) (1.08)!= 4205,890
b) When $300 000 has been reached, 300 000 ==> 300 000=100000(1.08)
3=(1.08) Taking logarithms to base 10 on both sides
log 3=log (1.08)
log 3=nlog (1.08)
log3
=143
log1.08
Hence it will take 15 years to reach more than $300 000
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Likely Examination Questions

According to a research study, parents with young children slept 6.4 hours each night last year, on average. a random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. this data has a sample standard deviation of 0.9. (assume that the scores are normally distributed.) researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year. the null and alternative hypotheses are h0: μ=6.4 and ha: μ> 6.4, which is a right-tailed test. the test statistic is determined to be t0=1.89 using the partial t-table below, determine the critical value(s). if there is only one critical value, leave the second answer box blank.