Exponential Function Solving - Growth (Continuous) - Equation to Time

Level 1

This math topic focuses on solving exponential growth equations related to various real-world contexts, such as population growth, financial investments, and social media metrics, using continuous growth models. The problems require the application of logarithmic functions to determine time variables, emphasizing understanding and manipulation of exponential and logarithmic expressions to isolate and solve for 't' (time). These equations feature scenarios like population of bacteria, savings account interest accumulation, increase in social media views, credit card debt growth, rabbit population increase, app downloads, and more. Each problem presents a formula based on the exponential growth concept and offers multiple-choice solutions.

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Exponential Function Solving - Growth (Continuous) - Equation to Time Worksheet

Exponential Function Solving - Growth (Continuous) - Equation to Time

Solve for the time given this model of a continuous growth of a bacteria population?

A LaTex expression showing 1,214 =900 times e to the power of (0.05 times t)

a $A LaTex expression showing 1 + t = +r over \ln{\frac{P {P sub 0 }}}$

b $A LaTex expression showing 1 + t = +\frac{\ln{P times P sub 0 }}{r}$

c $A LaTex expression showing t = +\ln{\frac{P over P sub 0 }}{r}$

d $A LaTex expression showing 6 + t = +\frac{\ln{P times P sub 0 }}{r}$

Solve for the time given this model of a continuously compounding growth of money in a savings account?

A LaTex expression showing 1,372 =800 times e to the power of (0.06 times t)

a $A LaTex expression showing 4 + t = +\frac{\ln{P times P sub 0 }}{r}$

b $A LaTex expression showing t = +\ln{\frac{P over P sub 0 }}{r}$

c $A LaTex expression showing 0 + t = +r over \ln{\frac{P {P sub 0 }}}$

d $A LaTex expression showing 9 + t = +\frac{\ln{P times P sub 0 }}{r}$

Solve for the time given this model of a continuous exponential growth of social media post views?

A LaTex expression showing 940 =600 times e to the power of (0.05 times t)

a $A LaTex expression showing t = +\ln{\frac{V over V sub 0 }}{r}$

b $A LaTex expression showing 3 + t = +\frac{\ln{V times V sub 0 }}{r}$

c $A LaTex expression showing 2 + t = +r over \ln{\frac{V {V sub 0 }}}$

d $A LaTex expression showing 0 + t = +r over \ln{\frac{V {V sub 0 }}}$

Solve for the time given this model of a growth of debt on a credit card with continuous compounding?

A LaTex expression showing 514 =300 times e to the power of (0.06 times t)

a $A LaTex expression showing 9 + t = +r over \ln{\frac{D {D sub 0 }}}$

b $A LaTex expression showing t = +\ln{\frac{D over D sub 0 }}{r}$

c $A LaTex expression showing 4 + t = +r over \ln{\frac{D {D sub 0 }}}$

Solve for the time given this model of a continuous growth of a rabbit population?

A LaTex expression showing 688 =500 times e to the power of (0.04 times t)

a $A LaTex expression showing 5 + t = +r over \ln{\frac{P {P sub 0 }}}$

b $A LaTex expression showing t = +\ln{\frac{P over P sub 0 }}{r}$

c $A LaTex expression showing 6 + t = +\frac{\ln{P times P sub 0 }}{r}$

d $A LaTex expression showing 9 + t = +\frac{\ln{P times P sub 0 }}{r}$

Solve for the time given this model of a continuously compounding growth of app downloads?

A LaTex expression showing 866 =800 times e to the power of (0.04 times t)

a $A LaTex expression showing t = +\ln{\frac{A over A sub 0 }}{r}$

b $A LaTex expression showing 8 + t = +r over \ln{\frac{A {A sub 0 }}}$

c $A LaTex expression showing 4 + t = +\frac{\ln{A times A sub 0 }}{r}$

Solve for the time given this model of a continuous exponential growth of social media post views?

A LaTex expression showing 514 =300 times e to the power of (0.09 times t)

a $A LaTex expression showing 2 + t = +r over \ln{\frac{V {V sub 0 }}}$

b $A LaTex expression showing 8 + t = +\frac{\ln{V times V sub 0 }}{r}$

c $A LaTex expression showing t = +\ln{\frac{V over V sub 0 }}{r}$

d $A LaTex expression showing 7 + t = +r over \ln{\frac{V {V sub 0 }}}$

Solve for the time given this model of a growth of debt on a credit card with continuous compounding?

A LaTex expression showing 1,214 =900 times e to the power of (0.06 times t)

a $A LaTex expression showing 9 + t = +\frac{\ln{D times D sub 0 }}{r}$

b $A LaTex expression showing t = +\ln{\frac{D over D sub 0 }}{r}$

c $A LaTex expression showing 7 + t = +r over \ln{\frac{D {D sub 0 }}}$

d $A LaTex expression showing 5 + t = +r over \ln{\frac{D {D sub 0 }}}$