8.EE.A.3 Math Practice Questions — Sports Academy Games

Practice playmedium

Let $f(t) = 8e^{3t} + 50$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(2)$ ?

Substitute $t = 2$ : $f(2) = 8e^{6} + 50$ . Since $e^{6} \approx 403.4$ , $f(2) \approx 8(403.4) + 50 = 3{,}277 \approx 3 \times 10^{3}$ .

Practice playeasy

$9 \times 10^5$ is how many times as large as $3 \times 10^2$ ?

$\dfrac{9 \times 10^5}{3 \times 10^2} = 3 \times 10^3 = 3{,}000$ .

Practice playmedium

Let $f(t) = 4e^{3t} + 200$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(3)$ ?

Substitute $t = 3$ : $f(3) = 4e^{9} + 200$ . Since $e^{9} \approx 8{,}103$ , $f(3) \approx 4(8{,}103) + 200 = 32{,}612 \approx 3 \times 10^{4}$ .

Practice playeasy

$0.0075 = c \times 10^{-3}$ . What is $c$ ?

Moving the decimal in $0.0075$ three places right gives $7.5$ , so $c = 7.5$ .

Practice playmedium

Let $f(t) = 4e^{2t} + 50$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(4)$ ?

Substitute $t = 4$ : $f(4) = 4e^{8} + 50$ . Since $e^{8} \approx 2{,}981$ , $f(4) \approx 4(2{,}981) + 50 = 11{,}974 \approx 1 \times 10^{4}$ .

Practice playeasy

Write $4500$ as $a \times 10^n$ where $1 \le a < 10$ . What is $n$ ?

$4500 = 4.5 \times 10^3$ , so $n = 3$ .

Practice playhard

Let $f(t) = 3e^{2t} + 10$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(5)$ ?

Substitute $t = 5$ : $f(5) = 3e^{10} + 10$ . Since $e^{10} \approx 22{,}026$ , $f(5) \approx 3(22{,}026) + 10 = 66{,}088 \approx 7 \times 10^{4}$ .

Practice playeasy

$(2 \times 10^3)(3 \times 10^4) = 6 \times 10^n$ . What is $n$ ?

Multiply coefficients ( $2 \cdot 3 = 6$ ) and add exponents: $3 + 4 = 7$ , so $n = 7$ .

8.EE.A.3 math practice. Learn by doing.

Skills aligned to 8.EE.A.3

Evaluating exponential functions

Scientific notation

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