Question

practice using the exponential growth formula by completing the table below.
original amount\tgrowth rate per year\tnumber of years, x\tfinal amount after x years of growth
2100\t11%\t35\t

complete the table below.
original amount\tgrowth rate per year\tnumber of years, x\tfinal amount after x years of growth
2100\t11%\t35\t
(round to the nearest whole number as needed.)

Explanation:

Step1: Recall the exponential growth formula

The exponential growth formula is $A = P(1 + r)^x$, where $A$ is the final amount, $P$ is the original amount, $r$ is the annual growth rate (in decimal form), and $x$ is the number of years.

Step2: Convert the growth rate to decimal

The growth rate is $11\%$, so in decimal form, $r = \frac{11}{100} = 0.11$.

Step3: Identify the values of $P$, $r$, and $x$

We have $P = 2100$, $r = 0.11$, and $x = 35$.

Step4: Substitute the values into the formula

Substitute into $A = P(1 + r)^x$:
$A = 2100(1 + 0.11)^{35}$
First, calculate $(1 + 0.11) = 1.11$. Then, calculate $1.11^{35}$. Using a calculator, $1.11^{35} \approx 39.1948$.

Step5: Calculate the final amount

Multiply $2100$ by $39.1948$:
$A = 2100 \times 39.1948 \approx 82309.08$

Step6: Round to the nearest whole number

Rounding $82309.08$ to the nearest whole number gives $82309$.

Answer:

82309