Question

(1 point) Give the starting value aa, the growth/decay rate r, and the continuous growth/decay rate k. If there is exponential decay your growth rates should negative.

Q=9⋅2^t/6has:

a=

r=

k=

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(1 point) Write the exponential function y=6(1.34)^t in the form y=ae^kt.

(a) Once you have rewritten the formula, give kk accurate to at least four decimal places.
k= help (numbers)

If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual and continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing decay the negative rate is implied).

(b) The annual GROWTH? OR DECAY?(CHOOSE ONE) decay ____ rate is  % per year (round to the nearest 0.01%).

(c) The continuous GROWTH? OR DECAY?(CHOOSE ONE) growth decay ___ rate is  % per year (round to the nearest 0.01%).

Please give me correct answer; no quessing game.

Answer 1

(a)

$y=6e^{t \ln (1.34)}$

in the form of

$y=ae^{t k}$

$a=6$

$k=\ln(1.34)$

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If $t$ measure the years then we observe that,as $t$ increase $y$ increase exponentially, i.e the exponential function is growing.

Now,

(b) $y=6(1.34)^t=6(1+0.34)^t$

In the form of,

$y=(1+r)^t$

and hence the annual growth rate is,

$r=0.34$

which is,

$0.34\times 100=34 \%$ per year

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(c) We have,

$y=6e^{t \ln(1.34)}$

The continous growth rate is,$\ln(1.34) \approx 0.29267$

or,

$29.26 \%$