The annual growth rate to the nearest percent will be 6%
Exponential growth
- Exponential growth is a process that increases quantity over time.
- It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself
- Exponential growth is a growth whose rate becomes ever more rapid in proportion to the growing total number or size.
How to solve this problem?
The steps are as follow:
- Based on the given conditions, formulate: [tex]100000 * (1+x)^{5}=135000[/tex]
- Reduce the greatest common factor on both sides of the equation:[tex]20* (1+x)^{5} = 27[/tex]
- Rearrange all nonzero terms to the left side of the equation:[tex]20(1+x)^{5}-27=0[/tex]
- Rewrite as the product of linear and/or quadratic factors:[tex]20(1+x)^{4}*(1+x)^{2}(1+x)-27=0\\[/tex]
- Multiply the monomials:[tex]20(1+x)^{2}(1+x)-27=0\\[/tex]
- Simplify using exponent rule with same base:[tex]20(1+x)^{4+1}-27=0[/tex]
- Rearrange unknown terms to the left side of the equation:[tex]20(1+x)^{4+1}=27[/tex]
- Rewrite the expression:[tex]20(x+1)^{4+1}=27[/tex]
- Divide both sides of the equation by the coefficient of variable:[tex](x+1)^{5}=\frac{27}{20}[/tex]
- By solving above expression we will get [tex]x=\frac{\sqrt[5]{135000}-10}{10} = 6[/tex]
So the annual growth rate to the nearest percent will be 6%
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