The expressions for the number of measles are y = a(1.05)^x and y = a(1.1)^x
Let the initial number of measles in 2000 be represented as:
Initial = a
The rate of increase is given as:
Rate, r = 5.3%
The number of measles in x years after 2000 is represented as:
y = a * (1 +r)^x
Substitute r = 5.3%
y = a * (1 + 5.3%)^x
So, we have:
y = a * (1 + 0.053)^x
Evaluate the sum
y = a * (1.053)^x
To express to the nearest hundredth, we approximate to 2 decimal places
y = a(1.05)^x
To express to the nearest tenth, we approximate to 1 decimal place
y = a(1.1)^x
Hence, the expressions for the number of measles are y = a * (1.05)^x and y = a * (1.1)^x
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