Answer:
Step-by-step explanation:
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The population will reach 32700 in 17.4 years.
The compound interest is interest you earn on interest. Compound interest is the interest calculated on the principle and the interest accumulated over the previous period.
For the given situation,
The population increase or decrease can be found by using compound interest method.
Population of the town, P = 14000
Rate of interest, R = 5%
The population to the nearest tenth year,A = 32700
Nearest tenth, so n = 1
let T be the time in years.
The formula for population increase by compound interest formula,
[tex]A=P[1+\frac{R}{n} ]^{nT}[/tex]
On substituting the above values,
⇒ [tex]32700=14000[1+\frac{5}{1} ]^{(1)T}[/tex]
⇒ [tex]32700 = 14000[1.05]^{T}[/tex]
⇒ [tex]1.05^{T} =\frac{32700}{14000}[/tex]
⇒ [tex]1.05^{T}=2.33[/tex]
Taking log on both sides,
⇒ [tex]Tlog1.05=log2.33[/tex]
⇒ [tex]T=\frac{log2.33}{log1.05}[/tex]
⇒ [tex]T=17.47[/tex] ≈ [tex]17.4[/tex]
Hence we can conclude that the population will reach 32700 in 17.4 years.
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