Task Sets: Express exponential solutions as logarithms - Common Core Math - HS Functions

Concepts

Which is the correct first step to solve $500 \cdot 2^{0.1t} = 4000$ ?

Take $\log$ of both sides: $\log(500 \cdot 2^{0.1t}) = \log(4000)$

Divide both sides by 500: $2^{0.1t} = 8$

Subtract 500 from both sides: $2^{0.1t} = 3500$

Divide both sides by 2: $500 \cdot 0.1t = 2000$

After isolating the exponential in a base-10 equation, you obtain
$10^{0.5t} = 47$ . Which expression correctly gives $0.5t$ ?

$0.5t = \ln(47)$

$0.5t = \log_{2}(47)$

$0.5t = \log(47)$

$0.5t = 47^{0.5}$

After writing $0.3t = \log(25)$ , complete the solution by dividing
both sides by $0.3$ . Round your answer to two decimal places.

Solve for $t$ : $200 \cdot 10^{0.3t} = 5000$ .

Divide both sides by 200, then convert to logarithmic form, then
divide by 0.3. Round your answer to two decimal places.

Solve for $t$ : $50 \cdot 2^{t/4} = 800$ .

Hint: $\log_2(16) = 4$ because $2^4 = 16$ . Give an exact integer answer.

Solve for $t$ : $1000 \cdot e^{0.05t} = 3000$ .

Use the $\ln$ key on your calculator. Round your answer to two
decimal places.

A student solves $300 \cdot e^{0.06t} = 900$ and writes:

Step 1: $e^{0.06t} = 3$
Step 2: $0.06t = \ln(3) \approx 1.099$
Step 3: $t \approx 1.099$ (answer)

What error did the student make?

The student should have used $\log$ instead of $\ln$ in Step 2.

The student forgot to divide by 0.06 in Step 3.

The student should have multiplied by 0.06 in Step 3.

Steps 1 and 2 are both incorrect.

Evaluate $t = \dfrac{\log(16)}{0.2}$ using a calculator.

Round your answer to two decimal places.