Sovi AI

題目

解題步驟

1. Understand the question

   given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease per unit of $x$, to the nearest tenth of a percent.
   $y = 400e^{0.198x}$

2. Explanation

   Step1: Identify growth/decay sign

   The exponent has a positive coefficient ($0.198$), so this is exponential growth.

   Step2: Convert to percentage rate

   For continuous exponential models $y = ae^{kx}$, the growth rate $r$ is calculated as $r = e^k - 1$.
   $r = e^{0.198} - 1$
   Calculate $e^{0.198} \approx 1.2187$, so $r \approx 1.2187 - 1 = 0.2187$

   Step3: Convert to percentage

   Multiply by 100 and round to nearest tenth: $0.2187 \times 100 = 21.87\% \approx 21.9\%$

3. Final answer

   This is exponential growth, with a percentage rate of increase of $21.9\%$ per unit of $x$.

答案

Question Analysis

OCR Text

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease per unit of $x$, to the nearest tenth of a percent.
$y = 400e^{0.198x}$

相關知識點

關聯題目

• use an area model to solve 31 × 26. multiply in the area model.

  Top-left cell: 180 Top-right cell: 6 Bottom-left cell: 600 Bottom-right cell: 20 Final product: 806

• 6. solve each equation. write each solution as a fraction and as a deci…

  | Equation | Solution (Fraction) | Solution (Decimal) | |----------|---------------------|--------------------| | $2x=3$ | $\frac{3}{2}$ | $1.5$ | | $5y=3$ | $\frac{3}{5}$ | $0.6$…

• Ok

  - Fila 2: Circular el par (5, 2). - Fila 3: Circular el par (3, 3) (o la tarjeta con 3 y la otra con 4 dibujos, pero los números son 3 y 3? Wait, la tercera fila: primera tarjeta …

• How do you solve pemdas

  It's basically just a checklist so you don't get mixed up when a math problem has a bunch of stuff going on at once. You just go down the list in order: 1. **P**arentheses: Do any…

• which number line models $-1 + (-14)$? add. $-1 + (-14) = \\square$

  \(-15\)

• 11 et 12

  The initial number of bacteria is 5. ### Turn 2 Answer Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières. Pour le **numéro 11**, on cherche le taux…

• find the following given the function. no spaces in answers. $y = \\fra…

  $y=3$

• 6.1 hw (ha2) (lms graded) describe how the graph of $g(x)=6\\cdot2^{x+1…

  The graph of $g(x)$ is shifted 4 units down and 1 unit(s) to the left of $f(x)$.

Sovi AI iOS

官網：mysovi.ai。題庫頁面網域：question-banks.mysovi.ai。iOS 應用透過 Apple App Store 提供。