Evaluating exponential functions Practice Questions (Grade 8)

Question 1medium

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

Question 2medium

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

Question 3medium

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

Question 4hard

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

Question 5hard

Let $f(t) = 6e^{2t}$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(5)$ ?

Substitute $t = 5$ : $f(5) = 6e^{10}$ . Since $e^{10} \approx 22{,}026$ , $f(5) \approx 6(22{,}026) = 132{,}156 \approx 1 \times 10^{5}$ .

Question 6hard

Let $f(t) = 5e^{3t} + 200$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(4)$ ?

Substitute $t = 4$ : $f(4) = 5e^{12} + 200$ . Since $e^{12} \approx 162{,}755$ , $f(4) \approx 5(162{,}755) + 200 = 813{,}975 \approx 8 \times 10^{5}$ .

Question 7hard

Let $f(t) = 2e^{3t} + 1{,}000$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(4)$ ?

Substitute $t = 4$ : $f(4) = 2e^{12} + 1{,}000$ . Since $e^{12} \approx 162{,}755$ , $f(4) \approx 2(162{,}755) + 1{,}000 = 326{,}510 \approx 3 \times 10^{5}$ .

Question 8hard

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

Substitute $t = 5$ : $f(5) = e^{15}$ . Since $e^{15} \approx 3{,}269{,}017$ , $f(5) \approx 3 \times 10^{6}$ .

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