Suppose y the number of cases of a disease is reduced by 7 p

Suppose y, the number of cases of a disease, is reduced by 7% per year. (a) If there are initially 10,000 cases, express y as a function of t, the number of years elapsed. y = (do not enter any commas in your formula) (b) How many cases will there be 5 years from now? cases. c) How long does it take to reduce the number of cases to 1000? years

Solution

Reduced by 7% per yr

So, at the end of a yr, it becomes 93% of the amount at the beginning of the year....

So, 93% is 93/100 or 0.93

So, we have :

y = y0 * (0.93)^t

So, with initial amount = 10000, we have :

y = 10000(0.93)^t ----> ANSWER

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b)
5 yrs from now :

10000(0.93)^5

6957 cases

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c)

1000 = 10000(0.93)^t

0.1 = 0.93^t

Taking log both sides :
ln(0.1) = ln(0.93^t)

ln(0.1) = t*ln(0.93)

t = ln(0.1)/ln(0.93)

t = 31.729 years