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Common Core Standard HSF-LE.A.4 Questions

For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

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Grade 11 Exponents CCSS: HSF-LE.A.4

Solve for

$x$ in

$3*10^(6x)=300$ .

Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4

What is the exact solution to

$10^(4x) = e^2 ?$

$x = 1/2 ln(e)$
$x = 1/2 log(e)$
$x = 2log(e/2)$
$x = log(e/2)$

Grade 11 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4

Water hyacinth is a plant that lives on top of water. In many areas, it is invasive. In these areas, without animals that eat it and with abundant food sources, it grows exponentially and can be modeled by the function

$H(t) = H_0 e^{a \ t}$ , where

$H$ is the surface area, in square feet, that it covers, and

$t$ is the time, measured in days, that it has been growing. If a certain river has a 4 foot square patch of water hyacinth on it, and then 13 days later it has grown to about 6.5 square feet, how many MORE days will it take for the water hyacinth to cover 12 square feet of the river's surface? Round answers to one decimal place.

15.9 days
16.7 days
27.1 days
42.7 days

Grade 11 Exponents CCSS: HSF-LE.A.4

Solve for

$x$ in

$11*e^(5x)=121$ .

Grade 11 Logarithms CCSS: HSF-BF.B.5, HSF-LE.A.4

$2^x=64$ is equivalent to which of the following?

$log_64 x=2$
$log_2 64=x$
$log_2 x=64$
$log_x 64=2$

Grade 12 Functions and Relations CCSS: HSA-CED.A.1, HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.B.5, HSF-LE.A.4

Travis gets a job which pays $22.50/h. Samantha gets a job that starts at $0.01/h and doubles every day. How long will it take before Samantha makes more per hour than Travis?

12 hours
12 days
Samantha will never make more than Travis
6 months

Grade 10 Exponents CCSS: HSF-BF.B.5, HSF-LE.A.4

Solve.

$e^x=92$

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