QuestionAugust 26, 2025

Let's try it! Evaluate the functions below. a(x)=(3)/(4)x-12 b(x)=4x^2-12x+50 c(t)=500(1+(.05)/(12))^12t a(18) b(3) c(5) a(-4) b(8) c(15)

Let's try it! Evaluate the functions below. a(x)=(3)/(4)x-12 b(x)=4x^2-12x+50 c(t)=500(1+(.05)/(12))^12t a(18) b(3) c(5) a(-4) b(8) c(15)
Let's try it! Evaluate the functions below. a(x)=(3)/(4)x-12 b(x)=4x^2-12x+50 c(t)=500(1+(.05)/(12))^12t a(18) b(3) c(5) a(-4) b(8) c(15)

Solution
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Answer

a(18) = 1.5, b(3) = 50, c(5) \approx 641.84, a(-4) = -15, b(8) = 210, c(15) \approx 1056.92 Explanation 1. Evaluate a(18) Substitute x = 18 into a(x) = \frac{3}{4}x - 12: a(18) = \frac{3}{4} \times 18 - 12 = 13.5 - 12 = 1.5 2. Evaluate b(3) Substitute x = 3 into b(x) = 4x^2 - 12x + 50: b(3) = 4 \times 3^2 - 12 \times 3 + 50 = 36 - 36 + 50 = 50 3. Evaluate c(5) Substitute t = 5 into c(t) = 500(1+\frac{.05}{12})^{12t}: c(5) = 500(1+\frac{.05}{12})^{60} \approx 500 \times 1.28368 \approx 641.84 4. Evaluate a(-4) Substitute x = -4 into a(x) = \frac{3}{4}x - 12: a(-4) = \frac{3}{4} \times (-4) - 12 = -3 - 12 = -15 5. Evaluate b(8) Substitute x = 8 into b(x) = 4x^2 - 12x + 50: b(8) = 4 \times 8^2 - 12 \times 8 + 50 = 256 - 96 + 50 = 210 6. Evaluate c(15) Substitute t = 15 into c(t) = 500(1+\frac{.05}{12})^{12t}: c(15) = 500(1+\frac{.05}{12})^{180} \approx 500 \times 2.11383 \approx 1056.92

Explanation

1. Evaluate $a(18)$<br /> Substitute $x = 18$ into $a(x) = \frac{3}{4}x - 12$: <br /> $a(18) = \frac{3}{4} \times 18 - 12 = 13.5 - 12 = 1.5$<br /><br />2. Evaluate $b(3)$<br /> Substitute $x = 3$ into $b(x) = 4x^2 - 12x + 50$: <br /> $b(3) = 4 \times 3^2 - 12 \times 3 + 50 = 36 - 36 + 50 = 50$<br /><br />3. Evaluate $c(5)$<br /> Substitute $t = 5$ into $c(t) = 500(1+\frac{.05}{12})^{12t}$:<br /> $c(5) = 500(1+\frac{.05}{12})^{60} \approx 500 \times 1.28368 \approx 641.84$<br /><br />4. Evaluate $a(-4)$<br /> Substitute $x = -4$ into $a(x) = \frac{3}{4}x - 12$: <br /> $a(-4) = \frac{3}{4} \times (-4) - 12 = -3 - 12 = -15$<br /><br />5. Evaluate $b(8)$<br /> Substitute $x = 8$ into $b(x) = 4x^2 - 12x + 50$: <br /> $b(8) = 4 \times 8^2 - 12 \times 8 + 50 = 256 - 96 + 50 = 210$<br /><br />6. Evaluate $c(15)$<br /> Substitute $t = 15$ into $c(t) = 500(1+\frac{.05}{12})^{12t}$:<br /> $c(15) = 500(1+\frac{.05}{12})^{180} \approx 500 \times 2.11383 \approx 1056.92$
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