Common Core Standard HSF-LE.A.2 Questions

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Grade 10 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2

Which formula represents the general term of the following sequence?

$1/2, -1, 2, -4, ...$

$a_n = 1/2 * 2^n$
$a_n = 1/2 * (-2)*(n-1)$
$a_n = 1/2 * -2^(n-1)$
$a_n = 1/2 * (-2)^(n-1)$

Grade 11 Exponents CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2

A lab keeps blood samples in a special fridge, which is kept at 0 °C, for a certain experiment. After the blood is initially taken from a patient and put in the fridge, its temperature is checked every 30 minutes for the first two hours. Below are those recordings. Which exponential function rule best describes this information?

$\ \ \ \ \ \ \ \ \ \ \ mathbf{"Time in Fridge (min)"} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{"Temperature (°C)"} \ \ \ \ \ \ \ \ \ \$
$30$	$19.2$
$60$	$10.5$
$90$	$5.8$
$120$	$3.2$

$f(t) = 35.2 * (-0.02)^t$
$f(t) = 35.2 * 0.98^t$
$f(t) = 6.8 * 1.08^t$
There is not enough information given in the table to find the function rule.

Grade 9 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2

Find the general term for the arithmetic sequence

$1/2, 7/2, 13/2, ...$

Grade 11 Exponents CCSS: HSF-LE.A.2

Create an exponential function of the form

$f(x) = ab^x,$ given the points

$(-2,5)$ and

$(3,10)$ . The numerical values of

$a$ and

$b$ have been rounded in the following answers.

$f(x) = 6.61*1.15^x$
$f(x) = 0.10*0.14^x$
$f(x) = 7.94*1.26^x$
At least three points are needed.

Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2

Which recursive function defines the sequence

$0, 2, 2, 10, 18, 58, 130, ...$ for

$n in N ?$

$t(1) = 0; \ \ t(n) = t(n-1) + n-2, \ n>1$
$t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4t(n-2), \ n>2$
$t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 2t(n-2), \ n>2$
$t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4(n-2), \ n>2$

Grade 11 Exponents CCSS: HSF-LE.A.2

Given the points

$(1,2)$ and

$(8,9)$ , which of the following exponential functions could be created with them? The numerical values in the function have been rounded.

$f(x) = 1.41*1.42^x$
$f(x) = 1.61*1.24^x$
$f(x) = 2.74*1.16^x$
All of the above.

Grade 10 Exponents CCSS: HSF-LE.A.2

$20,000 is invested at 6% interest, compounded quarterly. Approximately how many years will it take for the investment to double in value?

11.6
5
6.2
1.2

Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2

Which of the following recursive functions defines the sequence

$5,8,11,14,... ?$ Assume

$n in NN$ .

$t(1) = 3; \ \ t(n) = t(n-1) + 5, \ n>1$
$t(1) = 5, \ \ t(n) = t(n-1) - 3, \ n>1$
$t(1) = 5, \ \ t(n) = t(n-1) + 3, \ n>1$
$t(2) = 8, \ \ t(n) = t(n-2) + 6, \ n>2$

Grade 11 Exponents CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2

There are 20 rabbits living on an island, and the population triples every year. Which of the following functions correctly models this situation, where

$P$ is the population of rabbits, and

$t$ is the number of years since the current population count?

$P(t) = 20 + 3^t$
$P(t) = 20t^3$
$P(t) = 3t + 2$
$P(t) = 20*3^t$

Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2

Given the sequence

$1,4,16,64,256,...$ , which of the following correctly defines this sequence in a recursive form? Assume that

$n in NN$ .

$t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1$
$t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1$
$t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1$
$t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1$

Grade 11 Exponents CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2

There is a 100 g sample of Sodium-24 sitting in a secure storage box. After 15 hours, there is only 50 g left. Which function best describes this relationship between the amount of Sodium-24,

$S$ , and the time that has elapsed, in hours,

$t$ ?

$S(t) = 100*(1/2)^(15t)$
$S(t) = 100 e^(-0.046t)$
$S(t) = 50*(1/2)^(15t)$
$S(t) = 50 e^(-0.5t)$

Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2

Find the recursive form of the sequence

$10, 5, 0, -5, -10,...$ Assume

$n in NN$ .

$t(1) = 10; \ \ t(n) = -t(n-1) + 5, \ n>1$
$t(1) = 10; \ \ t(n) = -5 + t(n-1), \ n>1$ .
$t(1) = 10; \ \ t(n) = 10 - t(n-1), \ n>1$ .
$t(1) = 10; \ \ t(n) = t(n-1) - 5, n>1$

Grade 9 Functions and Relations CCSS: HSF-LE.A.2

The following table shows some of the values for the linear function

$f(x)$ . Find the correct function rule.

$\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \$
$-3$	$-17/2$
$-1$	$-15/2$
$1$	$-13/2$
$3$	$-11/2$