Sovi AI

Sovi AI

写真で学ぶ問題サポート

6.1 hw (ha2) savvas realize savvas realize due feb 9 11:59 pm 6.1 hw (h…

The function $y=130 \cdot 2.9^t$ represents exponential **growth**. Rewriting the base in terms of the rate of growth or decay results in the function $y = 130 \cdot (1+1.9)^t$. I…

カテゴリ: calculus 更新日: 2026-02-09

問題

6.1 hw (ha2)
savvas realize
savvas realize
due
feb 9 11:59 pm
6.1 hw (ha2) (lms graded)
determine whether the function represents exponential growth or decay. write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay
$y=130\\cdot 2.9^t$

the function $y = 130\\cdot 2.9^t$ represents exponential ____. rewriting the base in terms of the rate of growth or decay results in the function $y = 130\\cdot(1+\\square)^t$. in this function, $r=\\square$ which indicates that
the value of y __ by __ % each time period.
help me solve this view an example get more help
clear all check answer
review progress
question 8 of 16 block next

解法ステップ

  1. Understand the question

    6.1 hw (ha2)
    savvas realize
    savvas realize
    due
    feb 9 11:59 pm
    6.1 hw (ha2) (lms graded)
    determine whether the function represents exponential growth or decay. write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay
    $y=130\\cdot 2.9^t$

    the function $y = 130\\cdot 2.9^t$ represents exponential ____. rewriting the base in terms of the rate of growth or decay results in the function $y = 130\\cdot(1+\\square)^t$. in this function, $r=\\square$ which indicates that
    the value of y __ by __ % each time period.
    help me solve this view an example get more help
    clear all check answer
    review progress
    question 8 of 16 block next

  2. Explanation

    Step1: Identify growth/decay

    For $y = a \cdot b^t$, if $b>1$, it is growth. Here $b=2.9>1$, so growth.

    Step2: Rewrite base as $1+r$

    $b = 1+r \implies 2.9 = 1+r$
    $r = 2.9 - 1 = 1.9$

    Step3: Convert $r$ to percentage

    $1.9 \times 100 = 190\%$, so $y$ increases by 190% per period.

  3. Final answer

    The function $y=130 \cdot 2.9^t$ represents exponential growth. Rewriting the base in terms of the rate of growth or decay results in the function $y = 130 \cdot (1+1.9)^t$. In this function, $r=1.9$ which indicates that the value of $y$ increases by 190% each time period.

答え

Answer

The function $y=130 \cdot 2.9^t$ represents exponential growth. Rewriting the base in terms of the rate of growth or decay results in the function $y = 130 \cdot (1+1.9)^t$. In this function, $r=1.9$ which indicates that the value of $y$ increases by 190% each time period.

Explanation

Step1: Identify growth/decay

For $y = a \cdot b^t$, if $b>1$, it is growth. Here $b=2.9>1$, so growth.

Step2: Rewrite base as $1+r$

$b = 1+r \implies 2.9 = 1+r$
$r = 2.9 - 1 = 1.9$

Step3: Convert $r$ to percentage

$1.9 \times 100 = 190\%$, so $y$ increases by 190% per period.

Question Image

Click to enlarge

Question Analysis

Subject mathematics
Sub Subject calculus
Education Level high school
Difficulty unspecified
Question Type calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-09T20:31:42

OCR Text

Show OCR extraction
6.1 hw (ha2)
savvas realize
savvas realize
due
feb 9 11:59 pm
6.1 hw (ha2) (lms graded)
determine whether the function represents exponential growth or decay. write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay
$y=130\\cdot 2.9^t$

the function $y = 130\\cdot 2.9^t$ represents exponential ____. rewriting the base in terms of the rate of growth or decay results in the function $y = 130\\cdot(1+\\square)^t$. in this function, $r=\\square$ which indicates that
the value of y ____ by ____ % each time period.
help me solve this  view an example  get more help
clear all  check answer
review progress
question 8 of 16  block  next

関連トピック

mathematicscalculuscalculationhigh schoolturns-1

関連問題

Sovi AI iOS

公式サイトは mysovi.ai。問題ページは question-banks.mysovi.ai で配信。iOS アプリは Apple App Store で提供。

App Store で入手 カテゴリ: 微積分