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Answer:
[tex]P_1=11.7\\P_2=15.21\\P_n=9\cdot1.3^n\\P_{10}\approx124.07[/tex]
Step-by-step explanation:
An exponential function can be written in the form ...
y = a·b^x
where x is the independent variable, b is the common ratio, and 'a' is the initial value (when x=0). The "common ratio" is the ratio of each term to the one before. For example, b = P₁/P₀.
Here, you are told the initial value (P₀) is a=9, and the common ratio is b=1.3. The independent variable is given as n, so your population formula is ...
P(n) = 9·1.3^n
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You are asked for values when n = 1, 2, and 10. Since you know the common ratio, you can simply multiply P₀ by 1.3 to get P₁:
P₁ = 1.3·P₀ = 1.3·9 = 11.7
Similarly, ...
P₂ = 1.3·P₁ = 1.3·11.7 = 15.21
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You could continue up to P₁₀, but it is easier to use a calculator to evaluate the exponential function.
P(10) = 9·1.3¹⁰ ≈ 124.07
