Question

I need help I can’t understand this

Answer 1

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Answer:

  $P_1=11.7\\P_2=15.21\\P_n=9\cdot1.3^n\\P_{10}\approx124.07$

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